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Class of error correction codes
Permutation codes are a family of error correction codes that were introduced first by Slepian in 1965. and have been widely studied both in Combinatorics
Permutation_code
Mathematical version of an order change
In mathematics, a permutation of a set can mean one of two different things: an arrangement of its members in a sequence or linear order, or the act or
Permutation
Ordering of binary values, used for positioning and error correction
alternative name for the "reflected binary code"; one of those also lists "minimum error code" and "cyclic permutation code" among the names. A 1954 patent application
Gray_code
Scheme for numbering permutations
Lehmer code is a particular way to encode each possible permutation of a sequence of n numbers. It is an instance of a scheme for numbering permutations and
Lehmer_code
Subpermutation of a longer permutation
theoretical computer science, a (classical) permutation pattern is a sub-permutation of a longer permutation. Any permutation may be written in one-line notation
Permutation_pattern
Exact statistical hypothesis test
A permutation test (also called re-randomization test or shuffle test) is an exact statistical hypothesis test. A permutation test involves two or more
Permutation_test
Transmission of language with brief pulses
possible permutations of 1, 2, 3, and 4 dits and dahs (Russian Ы is used as Bulgarian Ь, Russian Ь is used as Bulgarian Ъ). Russian requires two more codes, for
Morse_code
Algorithm for shuffling a finite sequence
until no elements remain. The algorithm produces an unbiased permutation: every permutation is equally likely. The modern version of the algorithm takes
Fisher–Yates_shuffle
Sequence where any order is equally likely
set of objects. The use of random permutations is common in games of chance and in randomized algorithms in coding theory, cryptography, and simulation
Random_permutation
Operator used to vary the programming of chromosomes from one generation to the next
OCLC 654380156. Yu, Xinjie; Gen, Mitsuo (2010). "Variation Operators for Permutation Code". Introduction to Evolutionary Algorithms. Decision Engineering. London:
Crossover (evolutionary algorithm)
Crossover_(evolutionary_algorithm)
Class of functions in cryptography
cryptography, a pseudorandom permutation (PRP) is a function that cannot be distinguished from a random permutation (that is, a permutation selected at random with
Pseudorandom_permutation
Combinatorial algorithm
F. Trotter that generates all of the permutations of n {\displaystyle n} elements. Each two adjacent permutations in the resulting sequence differ by swapping
Steinhaus–Johnson–Trotter algorithm
Steinhaus–Johnson–Trotter_algorithm
Computer communications authentication algorithm
keyed-hash message authentication code or hash-based message authentication code) is a specific type of message authentication code (MAC) involving a cryptographic
HMAC
1994 science fiction novel by Greg Egan
Permutation City is a 1994 science-fiction novel by Greg Egan that explores many concepts, including quantum ontology, through various philosophical aspects
Permutation_City
Type of gradient noise in computer graphics
implementation worked on a 256-node grid and so included the following permutation table: int permutation[] = { 151, 160, 137, 91, 90, 15, 131, 13, 201, 95, 96, 53
Perlin_noise
Pair of positions in a sequence where two elements are out of sorted order
that are out of their natural order. Let π {\displaystyle \pi } be a permutation. There is an inversion of π {\displaystyle \pi } between i {\displaystyle
Inversion (discrete mathematics)
Inversion_(discrete_mathematics)
Sorting algorithm
as permutation sort and stupid sort) is a sorting algorithm based on the generate and test paradigm. The function successively generates permutations of
Bogosort
Process of mapping a continuous set to a countable set
(Section VI.C and Appendix B) Berger, T. (1972). "Optimum quantizers and permutation codes". IEEE Transactions on Information Theory. 18 (6): 759–765. Bibcode:1972ITIT
Quantization (signal processing)
Quantization_(signal_processing)
Set of cryptographic hash functions
sponge construction. The sponge construction is based on a pseudorandom permutation, and allows inputting ("absorbing" in sponge terminology) any amount
SHA-3
Scheme for controlling errors in data over noisy communication channels
(15 August 1995). "Weight Distributions for Turbo Codes Using Random and Nonrandom Permutations". TDA Progress Report. 122: 42–122. Bibcode:1995TDAPR
Error_correction_code
Polynomial that permutes a ring
In mathematics, a permutation polynomial (for a given ring) is a polynomial that acts as a permutation of the elements of the ring, i.e. the map x ↦ g
Permutation_polynomial
Method of generating all permutations of n objects
possible permutations of n objects. It was first proposed by B. R. Heap in 1963. The algorithm minimizes movement: it generates each permutation from the
Heap's_algorithm
High-performance forward error correction codes
convolutional code (RSC code). The third sub-block is n/2 parity bits for a known permutation of the payload data, again computed using an RSC code. Thus, two
Turbo_code
mathematics and computer science, a stack-sortable permutation (also called a tree permutation) is a permutation whose elements may be sorted by an algorithm
Stack-sortable_permutation
Type of matrix factorization
multiplication and matrix decomposition). The product sometimes includes a permutation matrix as well. LU decomposition can be viewed as the matrix form of
LU_decomposition
Class of error-correcting code
C2 are equivalent. Lemma: Any linear code is permutation equivalent to a code which is in standard form. A code is defined to be equidistant if and only
Linear_code
Family of linear error-correcting codes
matrices can be mutated into equivalent non-systematic codes by the following operations: Column permutations (swapping columns) Elementary row operations (replacing
Hamming_code
Type of Morse code operating signal
The Q-code is a standardised collection of three-letter codes that each start with the letter "Q". It is an operating signal initially developed for commercial
Q_code
Peirce's criterion Pensim2 – an econometric model Percentage point Permutation code Permutation test – redirects to Resampling (statistics) Pharmaceutical statistics
List_of_statistics_articles
Three-letter air-travel designation for airports and cities
combinations; a three-letter system of airport codes was implemented. This system allowed for 17,576 permutations, assuming all letters can be used in conjunction
IATA_airport_code
Sporadic simple group
M24. The group M24 also is the permutation automorphism group of the binary Golay code W, i.e., the group of permutations of coordinates mapping W to itself
Mathieu_group_M24
Numeral system in combinatorics
digits that can be converted to a permutation of n elements in a straightforward way, either using them as Lehmer code or as inversion table representation;
Factorial_number_system
Decryption of World War II cipher
spotted this phenomenon. The re-use of a permutation in the German Air Force METEO code as the Enigma stecker permutation for the day. Mavis Lever, a member
Cryptanalysis_of_the_Enigma
Rules by which information encoded within genetic material is translated into proteins
(all permutations of the four bases, read three at a time). He named this DNA–protein interaction (the original genetic code) as the "diamond code". In
Genetic_code
Approach to software development
Programming by permutation, sometimes called "programming by accident" or "shotgunning", is an approach to software development wherein a programming
Programming_by_permutation
Natural number
one of 26 sporadic finite simple groups, defined as the 3-transitive permutation representation on 22 points. There are also 22 regular complex apeirohedra
22_(number)
Cipher design construction
In cryptography, an SP-network, or substitution–permutation network (SPN), is a series of linked mathematical operations used in block cipher algorithms
Substitution–permutation network
Substitution–permutation_network
Purported set of secret messages encoded within the Hebrew text of the Torah
is in fact effectively nothing more than further increased number of permutations, employing a massive application of the look-elsewhere effect. The 13th-century
Bible_code
Method of encryption
In cryptography, a transposition cipher (also known as a permutation cipher) is a method of encryption which scrambles the positions of characters (transposition)
Transposition_cipher
Index of articles associated with the same name
for derivatives, used in thermodynamics Cyclic code, linear codes closed under cyclic permutations Cyclic convolution, a method of combining periodic
Cyclic_(mathematics)
Stream cipher
two parts: A permutation of all 256 possible bytes (denoted "S" below). Two 8-bit index-pointers (denoted "i" and "j"). The permutation is initialized
RC4
Five sporadic simple groups
introduced by Émile Mathieu (1861, 1873). They are multiply transitive permutation groups on 11, 12, 22, 23 or 24 objects. They are the first sporadic simple
Mathieu_group
Algorithm for solving various problems in computational group theory
This algorithm can find the order of a finite permutation group, determine whether a given permutation is a member of the group, and other tasks in polynomial
Schreier–Sims_algorithm
Natural number
the 12th. The "mirror property" is fulfilled when 73 has a mirrored permutation of its digits (37) that remains prime. Similarly, their respective prime
73_(number)
Mapping arbitrary data to fixed-size values
Therefore, it is more suited to hardware or microcode implementation. Unique permutation hashing has a guaranteed best worst-case insertion time. Standard multiplicative
Hash_function
Mathematics problem
of the permutation. Every permutation can be decomposed into disjoint cycles, that is, cycles which have no common elements. The permutation of the first
100_prisoners_problem
Source code that alters its instructions to the hardware while executing
not. This could be handled by producing four batches of code, one for each permutation and code bloat results. Alternatively, the weight and the skip arrays
Self-modifying_code
Function used in computer cryptography
A one-way permutation is a one-way function that is also a permutation—that is, a one-way function that is bijective. One-way permutations are an important
One-way_function
Family of quantum error correcting codes
the gnu code refers to a particular family of quantum error correcting codes, with the special property of being invariant under permutations of the qubits
Gnu_code
Type of error-correcting code using convolution
In telecommunication, a convolutional code is a type of error-correcting code that generates parity symbols via the sliding application of a boolean polynomial
Convolutional_code
Machine learning technique
by the rows of V {\displaystyle V} . To understand the permutation invariance and permutation equivariance properties of QKV attention, let A ∈ R m ×
Attention_(machine_learning)
System for displaying information by using different colors
color pair permutations. Continuous – the colors are ordered and form a smooth color gradient. Discrete – only a subset of a continuous color code are used
Color_code
Type of error correcting code
Codes, Fundamentals of Soft-Decision Decoding, Polar Codes, Properties of Polar Codes, Construction of Polar Codes, Monomial Codes and Permutations,
Polar_code_(coding_theory)
Arrangement of amino acid sequence
A circular permutation is a relationship between proteins whereby the proteins have a changed order of amino acids in their peptide sequence. The result
Circular permutation in proteins
Circular_permutation_in_proteins
new SLPS customers. SLPS performs “private permutation” for each company by transforming managed (.NET) code into a secure virtual machine (SVM) language
Microsoft Software Licensing and Protection Services
Microsoft_Software_Licensing_and_Protection_Services
Lock using symbols rather than a key
lock". Permutation padlock. Found in Google Books. [1] Improvement in permutation padlocks Google Books.[2] "IMPROVEMENT IN TUMBLERS FOR PERMUTATION-LOCKS"
Combination_lock
8th episode of the 5th season of The Big Bang Theory
"The Isolation Permutation" is the eighth episode of the fifth season of the American sitcom The Big Bang Theory and the 95th episode of the show overall
The_Isolation_Permutation
Cycle through all length-k sequences
while preserving order. This process defines the Standard Permutation. Write this permutation in cycle notation with the smallest position in each cycle
De_Bruijn_sequence
Type of cipher
text. For each key K, EK is a permutation (a bijective mapping) over the set of input blocks. Each key selects one permutation from the set of ( 2 n ) ! {\displaystyle
Block_cipher
Problem in computer science
for a non-square (rectangular) matrix, where it involves a complex permutation of the data elements, with many cycles of length greater than 2. In contrast
In-place_matrix_transposition
Cryptography construction
the block cipher a pseudorandom permutation, while 4 rounds are sufficient to make it a "strong" pseudorandom permutation (which means that it remains pseudorandom
Feistel_cipher
Type of linear error-correcting code
automorphism group of the perfect binary Golay code G23 (meaning the subgroup of the group S23 of permutations of the coordinates of F23 2 which leave G23
Binary_Golay_code
Decimal error detection code
number of digits be k. For example given the code 942 then k is 3 and a3 = m(2) = r2. Now define the permutation f : D5 → D5 f = ( e r r 2 r 3 r 4 s r s r
Verhoeff_algorithm
Sporadic simple group
was introduced by Mathieu (1861, 1873). It is a sharply 5-transitive permutation group on 12 objects. Burgoyne & Fong (1968) showed that the Schur multiplier
Mathieu_group_M12
Dialling code for London in the United Kingdom
By 1965, there were 350 local exchanges in London and the number of permutations that could be used for exchange names had been exhausted. With the change
020
Error-correcting codes used in wireless communication
can build a generator matrix for the RM(r, m) code, using vectors and their wedge product permutations up to r at a time v 0 , v 1 , … , v n , … , ( v
Reed–Muller_code
Method of bit-shuffling used to diffuse bits across S-box inputs
In cryptography, a permutation box (or P-box) is a method of bit-shuffling used to permute or transpose bits across S-boxes inputs, creating diffusion
Permutation_box
Wiki-based programming chrestomathy
Miller–Rabin primality test Morse code Numerical integration Pascal's triangle (draw) Perfect numbers Permutations Prime numbers (102 tasks) Primorial
Rosetta_Code
Matrix in linear algebra
transpose. Specifically, the commutation matrix K(m,n) is the nm × mn permutation matrix which, for any m × n matrix A, transforms vec(A) into vec(AT):
Commutation_matrix
Stream cipher
VMPC (Variably Modified Permutation Composition) for cryptography is a stream cipher similar to the well known and popular cipher RC4 designed by Ron
Variably Modified Permutation Composition
Variably_Modified_Permutation_Composition
Block cipher
size of 128, 192, or 256 bits. The cipher is a 32-round substitution–permutation network operating on a block of four 32-bit words. Each round applies
Serpent_(cipher)
American inventor (1927–2002)
Herbert Marvin Ohlman (1927–2002) is the inventor of permutation indexing, or Permuterm and is one of the pioneers of Information Science and Technology
Herbert_Marvin_Ohlman
Tables for the Data Encryption Standard
1 is always the most significant bit. This table specifies the input permutation on a 64-bit block. The meaning is as follows: the first bit of the output
DES_supplementary_material
Topics referred to by the same term
stored on mobile phone subscriber identity module (SIM) Substitution–permutation network, a mathematical operation used in cipher algorithms Sum-Product
SPN
Special kind of square matrix
unitriangular Toeplitz matrices, multiplied using F2 operations. They form the Cayley table of Z4 and correspond to powers of the 4-bit Gray code permutation.
Triangular_matrix
Practice and study of secure communication techniques
the Book of Cryptographic Messages, which contains the first use of permutations and combinations to list all possible Arabic words with and without vowels
Cryptography
invented here or (NIH) syndrome Premature optimization Programming by permutation (or "programming by accident", or "programming by coincidence") Reinventing
List of software anti-patterns
List_of_software_anti-patterns
Related mathematical concepts
In mathematics, the cycles of a permutation π of a finite set S correspond bijectively to the orbits of the subgroup generated by π acting on S. These
Cycles_and_fixed_points
Topics referred to by the same term
functions, a function is even if f(−x) = f(x) for all x Even and odd permutations, a permutation of a finite set is even if it is composed of an even number of
Even
Mathematical concept and applications in software development
special kind of cyclic permutation, which in turn is a special kind of permutation. Formally, a circular shift is a permutation σ of the n entries in the
Circular_shift
Method in cryptography
the purposes of the discussion below, the cipher is equivalent to a permutation of N integers {0, ... , N−1} where N is the size of the domain. One motivation
Format-preserving_encryption
Type of reversible cellular automaton
function is applied to the neighborhood of c to give a permutation σc. Then, this permutation σc is applied to the state of cell c at time t − 1, and
Second-order cellular automaton
Second-order_cellular_automaton
Polynomial in combinatorial mathematics
subsets of X and form a partition of X. The cycle structure of a permutation can be coded as an algebraic monomial in several (dummy) variables in the following
Cycle_index
Count of permutations by cycles
kind arise in the study of permutations. In particular, the unsigned Stirling numbers of the first kind count permutations according to their number of
Stirling numbers of the first kind
Stirling_numbers_of_the_first_kind
Block cipher
8 permutation tables, each a permutation of the numbers 0 to 255. Each round consists of 4 operations: XORing the block with one of the permutation tables
BassOmatic
Natural number
numbers between 5 and 31, inclusively, is 155. There are 155 primitive permutation groups of degree 81. OEIS: A000019 If one adds up all the primes from
155_(number)
Open-source software library developed by Yandex
among other features, attempts to solve for categorical features using a permutation-driven alternative to the classical algorithm. It works on Linux, Windows
CatBoost
Natural number
the reverse of any number that is divisible by three (or indeed, any permutation of its digits) is also divisible by three. This divisibility rule works
3
Authenticated encryption mode
is used with a block cipher that is indistinguishable from a random permutation; however, security depends on choosing a unique initialization vector
Galois/Counter_Mode
2x2x2 combination puzzle
Association". www.worldcubeassociation.org. Retrieved 2025-10-24. Methods for speedsolving the 2×2×2 code for enumerating all permutations of a Rubik's Cube
Pocket_Cube
German cipher machine during World War II
mathematician and cryptologist at the Polish Cipher Bureau, used the theory of permutations, and flaws in the German military-message encipherment procedures, to
Enigma_machine
Type of barcode
so the Patch Code symbols are a fixed length. There are six distinct permutations of the wide and narrow bars, so there are six Patch Codes. The patches
Patch_Code
Fast 8-bit hash function
requires only a few instructions, plus a 256-byte lookup table containing a permutation of the values 0 through 255. This hash function is a CBC-MAC that uses
Pearson_hashing
9th episode of the 9th season of The Big Bang Theory
"The Platonic Permutation" is the ninth episode of the ninth season of The Big Bang Theory. The 192nd episode overall, it first aired on CBS on November
The_Platonic_Permutation
Short story by Jorge Luis Borges
book ever written, or that might ever be written, and every possible permutation or slightly erroneous version of every one of those books. The narrator
The_Library_of_Babel
Number that permute or shift cyclically when multiplied by another number
corresponding fractions. The greatest common divisor (gcd) between any cyclic permutation of an m-digit integer and 10m − 1 is constant. Expressed as a formula
Transposable_integer
Study of analyzing information systems in order to discover their hidden aspects
Distinguishing algorithm – the attacker can distinguish the cipher from a random permutation. Academic attacks are often against weakened versions of a cryptosystem
Cryptanalysis
1998 esoteric programming language
Scheffer's cryptanalysis of Malbolge mentions six different cycles in the permutation. They are listed here: 33 ⇒ 53 ⇒ 45 ⇒ 119 ⇒ 78 ⇒ 49 ⇒ 87 ⇒ 48 ⇒ 123 ⇒
Malbolge
Authenticated encryption with associated data algorithm
construction is generally secure in the standard model and the ideal permutation model, for the single- and multi-user setting. However, similarly to
ChaCha20-Poly1305
Early unclassified symmetric-key block cipher
and trivially breakable. Permutation: finally, the 32 outputs from the S-boxes are rearranged according to a fixed permutation, the P-box. This is designed
Data_Encryption_Standard
PERMUTATION CODE
PERMUTATION CODE
Boy/Male
Irish American English
Helpful.
Boy/Male
Arabic, Muslim
Rockstar
Girl/Female
Tamil
Code
Surname or Lastname
English
English : occupational name for a watchman or guard, from Old English weard ‘guard’ (used as both an agent noun and an abstract noun).Irish : reduced form of McWard, an Anglicized form of Gaelic Mac an Bhaird ‘son of the poet’. The surname occurs throughout Ireland, where three different branches of the family are known as professional poets.Surname adopted by bearers of the Jewish surname Warshawski, Warshawsky or some other Jewish name bearing some similarity to the English name.Americanized form of French Guerin.The surname Ward was brought to North America from England independently by several different bearers in the 17th and 18th centuries. Nathaniel Ward (1578–1652), author of the MA legal code, was born in Haverhill, Suffolk, England, and emigrated to Agawam (Ipswich, MA) in 1633. William Ward was one of the original settlers of Sudbury, MA, in about 1638. Miles Ward came from England to Salem, MA, in about 1639. Thomas Ward (d. 1689) settled in Newport, RI, in 1671; among his descendants were two governors of colonial RI.
Boy/Male
Hindu, Indian, Jain, Marathi, Sanskrit, Sindhi, Tamil
Lines on Any Particular Raaga from Sanskrit; Permutations and Combinations of Parents; Aarya Cost King Ashoka's Birth
Boy/Male
American, Anglo, Australian, British, English, Irish
Cushion; Helpful; Pillow
Girl/Female
American, Australian, British, English, Irish
Cushion; Helpful
Girl/Female
Hindu
Code
Boy/Male
American, British, English, Irish
Helpful
Girl/Female
Tamil
Vyaapti | வà¯à®¯à®¾à®ªà®¤à¯€
Achievement, Omnipresence, Permeation
Vyaapti | வà¯à®¯à®¾à®ªà®¤à¯€
Girl/Female
Hindu
Achievement, Omnipresence, Permeation
Surname or Lastname
English
English : variant spelling of Coad.
Surname or Lastname
English
English : nickname for a person who insisted on a strict code of social behavior.German : topographic name for someone who lived on or by a hill, from Middle High German stickel ‘hill’, ‘slope’ + the suffix -er denoting an inhabitant; in the south an occupational name for someone who shapes and sets stakes in vineyards.
Female
Japanese
(1-儀, 2-典, 3-則, 4-法) Japanese unisex name NORI means 1) "ceremony, regalia," 2) "code, precedent," 3) "model, rule, standard," 4) "law, rule."
PERMUTATION CODE
PERMUTATION CODE
Girl/Female
Indian
Name of a star
Male
English
Exalted Father
Girl/Female
Gujarati, Hindu, Indian
Soul
Boy/Male
Indian
Trustworthy
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Punjabi, Sanskrit, Sikh, Telugu
Sprite of Hevan; Name of a Raga or Melody
Biblical
Ancients; chiefs
Girl/Female
Gujarati, Hindu, Indian, Sanskrit, Sindhi, Tamil
Gold; Goddess Parvati
Girl/Female
Biblical
Inquirer, examiner, dull observer.
Male
Greek
(Δείμος) Greek name DEIMOS means "fear, terror." In mythology, this is the name of a son of Ares and Aphrodite.
Female
Native American
Native American Shawnee name METHOATASKE means "turtle laying its eggs."
PERMUTATION CODE
PERMUTATION CODE
PERMUTATION CODE
PERMUTATION CODE
PERMUTATION CODE
n.
Any system of rules or regulations relating to one subject; as, the medical code, a system of rules for the regulation of the professional conduct of physicians; the naval code, a system of rules for making communications at sea means of signals.
n.
Long continuance.
n.
The arrangement of any determinate number of things, as units, objects, letters, etc., in all possible orders, one after the other; -- called also alternation. Cf. Combination, n., 4.
n.
The act of permeating, passing through, or spreading throughout, the pores or interstices of any substance.
n.
Barter; exchange.
n.
An unwritten code of law represented to have been given by God to Moses on Sinai.
v. t.
To signal by means of a flag waved from side to side according to a code adopted for the purpose.
n.
The act of drinking excessively; a drinking bout.
n.
Alt. of Perduration
n.
The act of permuting; exchange of the thing for another; mutual transference; interchange.
n.
The Jewish or Mosaic code, and that part of Scripture where it is written, in distinction from the gospel; hence, also, the Old Testament.
n.
Permutation.
a.
Proof against penetration or permeation by water; impervious to water; as, a waterproof garment; a waterproof roof.
a.
Enacting or threatening punishment; as, a penal statue; the penal code.
v. t.
Alteration in the order of a series; permutation.
n.
A collection or digest of laws; a code.
n.
The substitution of one root vowel for another, thus indicating a corresponding modification of use or meaning; vowel permutation; as, get, gat, got; sing, song; hang, hung.
n.
Hence, the code of ceremonies observed by an organization; as, the ritual of the freemasons.
n.
Any one of such possible arrangements.
n.
One of the opium alkaloids; a white crystalline substance, C18H21NO3, similar to and regarded as a derivative of morphine, but much feebler in its action; -- called also codeia.