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Pair of related error-correcting codes
In coding theory, the ternary Golay codes are two closely related error-correcting codes. The code generally known simply as the ternary Golay code is
Ternary_Golay_code
Topics referred to by the same term
Golay code may refer to: Binary Golay code, an error-correcting code used in digital communications Ternary Golay code (Golay) complementary sequences
Golay_code
Type of linear error-correcting code
binary Golay code is a type of linear error-correcting code used in digital communications. The binary Golay code, along with the ternary Golay code, has
Binary_Golay_code
Topics referred to by the same term
error-correcting code Ternary Golay code, an error-correcting code Places: Golay, Kutch, a village in Kutch, Gujarat, India Gola (disambiguation) Golay code (disambiguation)
Golay
Topics referred to by the same term
a data structure in computer science Ternary Golay code, a perfect [11, 6, 5] ternary linear code ?:, a ternary conditional operator used for basic conditional
Ternary
24-dimensional repeating pattern of points
the 1s of any codeword of the Golay code, and the ∓3 can appear in any position. The ternary Golay code, binary Golay code, and Leech lattice give very
Leech_lattice
Mathematical tool
function for the Mathieu group M12 and ternary Golay code as the Miracle Octad Generator does for M24 and binary Golay code, respectively. Instead of using a
Miracle_Octad_Generator
Swiss mathematician (1902–1989)
Discoverer of the famous binary and ternary Golay codes, which are perfect error-correcting codes that generalize the Hamming code. They were used in the Voyager
Marcel_J._E._Golay
Study of the properties of codes and their fitness
1, 2r – 1 – r, 3), and the [23,12,7] binary and [11,6,5] ternary Golay codes. Another code property is the number of neighbors that a single codeword
Coding_theory
Type of block code
Binary Golay code Cyclic redundancy check Eugene Prange Reed–Muller code Ternary Golay code Van Lint 1998, p. 76 Ryan & Lin 2009, pp. 108–109 Van Lint 1998
Cyclic_code
Quantum computing algorithm
Prakash, Shiroman (September 2020). "Magic state distillation with the ternary Golay code". Proceedings of the Royal Society A: Mathematical, Physical and Engineering
Magic_state_distillation
Pairs of sequences
(also called maximum length sequences or M-sequences) Ternary Golay code (Error-correcting code) Walsh-Hadamard sequences Zadoff–Chu sequence Donato,
Complementary_sequences
{\displaystyle (23,12)} binary Golay code over G F ( 2 ) {\displaystyle GF(2)} and the ( 11 , 6 ) {\displaystyle (11,6)} ternary Golay code over G F ( 3 ) {\displaystyle
Quadratic_residue_code
Logic puzzle
of the perfect ternary Golay code (Virtakallio-Golay code). At the same time, it is established that a static WA (i.e. weighting code) with the same parameters
Balance_puzzle
Class of error-correcting code
linear code is a sequence of dual Hamming codes. Some examples of linear codes include: Repetition code Parity code Cyclic code Hamming code Golay code, both
Linear_code
Sporadic simple group
cover 2.M12 is the automorphism group of the extended ternary Golay code, a dimension 6 length 12 code over the field of order 3 of minimum weight 6. In particular
Mathieu_group_M12
algorithm Binary Golay code Binary Goppa code Bipolar violation CRHF Casting out nines Check digit Chien's search Chipkill Cksum Coding gain Coding theory Constant-weight
List of algebraic coding theory topics
List_of_algebraic_coding_theory_topics
Sporadic simple group
ISBN 978-0-387-98585-5, MR 0920369 Thompson, Thomas M. (1983), From error-correcting codes through sphere packings to simple groups, Carus Mathematical Monographs
Conway_group_Co1
van Lint, and Johan Jacob Seidel [de] as the coset graph of the ternary Golay code. This graph is the Cayley graph of an abelian group. Among abelian
Berlekamp–Van Lint–Seidel graph
Berlekamp–Van_Lint–Seidel_graph
J. J. (1973), "A strongly regular graph derived from the perfect ternary Golay code", A Survey of Combinatorial Theory (Proc. Internat. Sympos., Colorado
Games_graph
Graph where every edge is in one triangle
J. J. (1973), "A strongly regular graph derived from the perfect ternary Golay code", A Survey of Combinatorial Theory (Proc. Internat. Sympos., Colorado
Locally_linear_graph
Natural number
number 24 also occurs in coding theory and finite group theory through the extended binary Golay code, a self-dual binary linear code with parameters [ 24
24_(number)
Book
binary Golay codes, and the ternary Golay codes. The second edition adds material on BCH codes, Reed–Solomon error correction, Reed–Muller codes, decoding
Introduction to the Theory of Error-Correcting Codes
Introduction_to_the_Theory_of_Error-Correcting_Codes
Natural number
vectors in the Leech lattice. The extended binary Golay code is an extension of the perfect binary Golay code B 23 {\displaystyle \mathbb {B} _{23}} , which
23_(number)
Geometrical structure
linear codes. There are other, subtler relationships between Euclidean sphere packing and error-correcting codes. For example, the binary Golay code is closely
Sphere_packing
Central computer component that executes instructions
employed more unusual representations such as bi-quinary coded decimal (base 2–5) or ternary (base 3). Nearly all modern CPUs represent numbers in binary
Central_processing_unit
TERNARY GOLAY-CODE
TERNARY GOLAY-CODE
Surname or Lastname
English
English : variant of Gulley.Possibly a variant of Irish Gooley.
Boy/Male
Celtic
Regal.
Surname or Lastname
English, French, Dutch, Polish, Czech, and Slovenian
English, French, Dutch, Polish, Czech, and Slovenian : from a Germanic personal name (see Bernhard). The popularity of the personal name was greatly increased by virtue of its having been borne by St. Bernard of Clairvaux (c.1090–1153), founder and abbot of the Cistercian monastery at Clairvaux.Americanized form of German Bernhard or any of the other cognates in European languages; for forms see Hanks and Hodges 1988.The first bearer of the name in Canada was from the Lorraine region of France. He is documented in Quebec city in 1666 as Jean Bernard. He and some of his descendants bore the secondary surnames Anse and Hanse, because his original forename must have been Hans (the German equivalent of French Jean, English John). Another bearer, from La Rochelle, is documented in Quebec city in 1676; and a third, from the Poitou region of France, was also documented in Quebec city, in 1713, with the secondary surname Léveillé. Other documented secondary names are Jolicoeur, Larivière, and Lajoie.
Girl/Female
American, Australian, Bengali, British, English, German, Indian, Kannada, Sindhi, Telugu
Gold; Gilded; Form of Golda
Boy/Male
African, American, Australian, British, Chinese, Christian, Czechoslovakian, Danish, Dutch, English, French, German, Indian, Irish, Latin, Polish, Swiss
Brave as a Bear; Bear; Courageous; Strong; Bear-brave
Girl/Female
Hindu, Indian
A River
Surname or Lastname
English (Cornwall)
English (Cornwall) : variant of Gulley.German : variant of Gohl, or in the south of Goll.
Male
English
 English form of Anglo-Saxon Beornheard, BERNARD means "bold as a bear." Compare with another form of Bernard.
Boy/Male
Indian, Sanskrit
Mooing of the Cow
Boy/Male
English American German
Strong as a bear. See also Bjorn.
Girl/Female
Indian, Parsi
Rose Water
Girl/Female
English
Gilded.
Male
French
 Norman French form of Old High German Bernhard, BERNARD means "bold as a bear." Compare with another form of Bernard.
Male
English
Compare with feminine Terry. English form of Norman French Thierri, TERRY means "first of the people; king of nations." Pet form of English Terence, possibly meaning "rub, turn, twist."Â
Girl/Female
Biblical
Passage, revolution.
Boy/Male
German
Bear; Courageous
Biblical
passage; revolution
Male
English
Stern Bear
Boy/Male
Hindu, Indian
Golden
Female
English
Variant spelling of English Terrie, TERRY means "harvester." Compare with masculine Terry.
TERNARY GOLAY-CODE
TERNARY GOLAY-CODE
Girl/Female
Muslim/Islamic
Unique
Girl/Female
American, Australian, Christian, Dutch, French, German, Hebrew, Scottish, Swedish
Gift from God; Female Version of John; The Lord is Gracious; Similar to Jane
Boy/Male
Hindu, Indian, Tamil
Strong; Brave
Boy/Male
Hebrew
Twin.
Girl/Female
Australian, Danish, German, Hebrew, Italian, Swedish
Pledged to God; God's Promise; God is My Oath
Girl/Female
American, British, English
Eye of the Day; Day's Eye
Boy/Male
Sikh
Diligence
Girl/Female
Indian
Sweet Sound
Girl/Female
American, Australian, British, Danish, English
Path; Way; Road
Girl/Female
Muslim/Islamic
Flower
TERNARY GOLAY-CODE
TERNARY GOLAY-CODE
TERNARY GOLAY-CODE
TERNARY GOLAY-CODE
TERNARY GOLAY-CODE
a.
Being of the third formation, order, or rank; third; as, a tertiary use of a word.
a.
Having the parts arranged by threes; as, ternate branches, leaves, or flowers.
pl.
of Tertiary
a.
The number three; three things together; a ternary.
a.
Doubly ternate, as when a petiole has three ternate leaflets.
a.
Possessing some quality in the third degree; having been subjected to the substitution of three atoms or radicals; as, a tertiary alcohol, amine, or salt. Cf. Primary, and Secondary.
n.
A ternion; the number three; three things taken together; a triad.
n. pl.
Palm leaves, prepared for being written upon with a style pointed with steel.
n.
The Tertiary era, period, or formation.
a.
Proceeding by threes; consisting of three; as, the ternary number was anciently esteemed a symbol of perfection, and held in great veneration.
n.
A ternary compound of oxygen and chlorine; as, plumbic oxychloride.
n.
A kind of heavy colored fabric, either all silk, or silk and worsted, or silk and cotton, often called terry velvet, used for upholstery and trimmings.
a. & n.
Same as Tertiary.
pl.
of Ternary
n.
A ternary compound of oxygen and sulphur.
a.
Containing, or consisting of, three different parts, as elements, atoms, groups, or radicals, which are regarded as having different functions or relations in the molecule; thus, sodic hydroxide, NaOH, is a ternary compound.
n.
A tertiary amine analogous to trimethylamine.
a.
Earlier than Tertiary.
a.
Containing ten; tenfold; proceeding by tens; as, the denary, or decimal, scale.
pl.
of Turbary