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	Ternary Golay code - Wikipedia, the free encyclopedia
		There are two closely related error-correcting codes known as ternary Golay codes.
		The code generally known simply as the ternary Golay code is a perfect (11, 6, 5) ternary linear code; the extended ternary Golay code is a (12, 6, 6) linear code obtained by adding a zero-sum check digit to the (11, 6, 5) code.
		The automorphism group of the extended ternary Golay code is 2.
	en.wikipedia.org /wiki/Ternary_Golay_code (188 words)

	PlanetMath: linear code
		Often in coding theory, a code's alphabet is taken to be a finite field.
		Though not sufficient for unique classification, a linear code's block length, dimension, and minimum distance are three crucial parameters in determining the strength of the code.
		binary code, ternary code, quaternary code, dimension of a linear code
	planetmath.org /encyclopedia/BinaryCode.html (183 words)

	PlanetMath: perfect code
		The list of classes of linear perfect codes is very short, including only trivial codes, Hamming codes (i.e.
		), and the binary and ternary Golay codes.
		This is version 2 of perfect code, born on 2004-06-04, modified 2004-06-08.
	planetmath.org /encyclopedia/PerfectCode.html (59 words)

	Golay code - Wikipedia, the free encyclopedia
		binary Golay code - for the binary (base 2) Golay code
		ternary Golay code - for the ternary (base 3) Golay code
		This is a disambiguation page: a list of articles associated with the same title.
	en.wikipedia.org /wiki/Golay_code (101 words)

	Decoding the Golay code by hand: Generalizations
		As a small example, consider the code where the information symbols are written on the vertices, and all other cells (edges, faces and the body) correspond to parity checks.
		If we are working with codes over other fields (or rings), the mask is replaced by a filter: a set of coefficients taken from the appropriate ring that are constant on the orbits of the stabilizer of a cell.
		It would, in general, be difficult to distinguish if the codes having the same weight distributions are equivalent, however from the manner in which they were constructed we can easily decide that many are.
	www.southernct.edu /~fields/DecodingGolay/generalizations.html (936 words)

	Decoding the Golay code by hand: Conclusions
		Thus an algorithm (essentially Polya counting) computing the minimum distance of the codes we have considered is possible for codes having dimensions much higher than would be practical for generic codes.
		M12 (the automorphism group of the extended ternary Golay code of length 12) is constucted from the group of a dodecahedron with certain additional "twists".
		Since this group and the extended binary Golay code are intimately related, it seems natural (in view of our construction) to consider whether there are natural geometric generators for M24 that can be viewed via the dodecahedron.
	www.southernct.edu /~fields/DecodingGolay/conclusions.html (873 words)

	[No title]
		The automorphism group of the binary (ternary) Golay code of length 24 (12) is the Mathieu group M_{24} (M_{12}) which is one of the 26 sporadic finite simple groups.
		Besides the costruction of good codes, we demonstrate a hand decoding of the binary Reed-Muller code of length 32 and dimension 16 by projecting it onto the binary Hamming code of length 8 and dimension 4 over GF(4).
		For lengths 36 and 38, we construct more codes than were previously known and for length 58 we construct several new codes which have previously unknown weight enumerators.
	www.math.louisville.edu /~jlkim/abs_the.html (880 words)

	Code Healing
		Prefix code - A prefix code is a code which meets the "prefix property", which is that no code word is a prefix of any other code word in the set.
		A code which uses code words {0,10,11} meets the prefix property; a code whose set is {0,1,10,11} does not because "1" is a prefix of both "10" and "11".
		In The Heart's Code, Dr. Paul Pearsall explains the theory code healing and science behind energy cardiology, the newly emerging field that is uncovering one of the most significant medical, social, code healing and spiritual discoveries of our time.
	www.wsddyy.com /codehealing.html (822 words)

	[No title]
		The rows of the {\it parity check matrix} of $C$ are a basis for the code, \[ C^* = \{ v \in GF(q)^n\ \ v\cdot c = 0,\ for \ all\ c \in C \}, \] called the {\it dual space} of $C$.
		The associated {\it toric code} $C$ is the evaluation code which is the image of the evaluation map $$ eval_T : V \rightarrow F^n, $$ where $x^e$ is the multi-index notation ($x=(x_1,...,x_d)$, $e=(e_1,...,e_d)$, and $x^e = x_1^{e_1}...x_d^{e_d}$), where $eval_T (f(x)) = (f(t_1),...,f(t_n))$, and where $T=\{t_1,...,t_n\}$.
		The cyclic code C associated to (g,n,F) is isomorphic as a vector space) to the principal ideal $(g)$ in the ring $R = F[x]/(x^n-1)$ generated by g.
	modular.math.washington.edu /sagesrc/sage/coding/linear_code.py.txt (1811 words)

	Families of Linear Codes
		Construct the quasi-twisted cyclic code of length n pasting together the constacyclic codes with parameter alpha generated by the polynomials in Gen.
		This function constructs the BCH code of designated distance d as the cyclic code with generator polynomial g(x) = lcm{ m_1(x),..., m_(d - 1)(x)} where m_i(x) is the minimum polynomial of alpha^(b + i - 1).
		The construction is similar to that of a doubly circulant code except that the first p rows are extended by a mod 2 while the p + 1-th row is extended by b mod 2.
	www.math.wayne.edu /answers/magma2.10/htmlhelp/text1336.htm (1470 words)

	CLASSICAL and QUANTUM INFORMATION THEORY
		C24 is a binary Golay code [24,12,8] is a code of length 24, dimension 12, and minimal distance 8 over the binary field F2.
		A common fundamental structure causes quantum-error-correcting codes to be based on GF(4), the hexacode H6 to be related to the Golay codes and Leech lattice, and an RNA code to be based on 4 nucleotides UGAC, taken 3 at a time.
		This is the generator matrix of the quantum code [[ 256, 0, 24 ]] as constructed by Steane.
	www.valdostamuseum.org /hamsmith/info.html (6749 words)

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		Universal Code (Post Code) - The Universal Code is a "post code" of the Universal Postal Union.
		List of ICD-9 codes E and V codes: External causes of injury and supplemental classification - ==E section -- External causes of injury==
		Ternary Golay code - There are two closely related error-correcting codes known as ternary Golay codes.
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	[No title]
		But the next significant result did not come until 1973, with Delsarte's famous theorem that the covering radius of a code is at most equal to the number of nonzero weights in the orthogonal code [P. Delsarte, Information and Control 23 (1973), 407--438; MR 48 #13453].
		A (binary) code $C$ is a subset of $V\coloneq{F}\sb 2\sp n$; the covering radius $R(C)$ of $C$ is the least integer $r$ such that the spheres of radius $r$ in the Hamming metric centered at the points of $C$ cover $V$.
		A code is called a weighted covering if the density at each point is at least one." If the density is exactly 1 at each point, the code is called a perfect weighted covering code.
	www.eng.tau.ac.il /~litsyn/skip.html (1787 words)

	PPI no. 2, 1995
		Abstract—The universal coding of memoryless sources is considered in the case where its redundancy depends on the number of different letters in the message to be encoded.
		Abstract—The characteristics of q-ary convolutional codes are investigated for the ensemble of codes where the codes are used for information transmission under the condition that there is artificial signal-like noise (jamming) in the channel and additive noise is absent.
		A decoding algorithm of the convolutional codes is proposed.
	www.ece.umd.edu /~abarg/ppi/contents/2-95-abstracts.html (607 words)

	Definition of a Code
		We define the ternary Golay code as a six-dimensional subspace of the vector space K^((11)), where K is GF(3).
		We construct the length 23 Golay code over GF(2) as a cyclic code by factorizing the polynomial x^(23) - 1 over GF(2) and constructing the cyclic code generated by one of the factors of degree 11.
		Given a positive integer d, and an integer b >= 1, this function constructs the BCH code of designated distance d having generator polynomial g(x) = lcm{ m_1(x),..., m_(d - 1)} where m_i(x) is the minimum polynomial of alpha^(b + i - 1), for i = 1,..., d - 1.
	www.math.wisc.edu /help/magma/text675.html (1917 words)

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	CiteULike: Decoding the ternary Golay code (Site not responding. Last check: 2007-11-01)
		A decoding algorithm is presented for the ternary (11, 6, 5) Golay code.
		This algorithm is an algebraic decoding and relies on solving the Newton identities associated with the syndromes of the code.
		@article{Higgs-Humphreys:IEEE_IT1993, abstract = {A decoding algorithm is presented for the ternary (11, 6, 5) Golay code.
	www.citeulike.org /user/danielaugot/article/523377 (129 words)

	Coding Theory: Third Assignment
		CT 3.5.2, another generator for the Golay code.
		CT 3.6.5 f, g, h, i, decoding for the extended Golay code.
		Use the ternary Golay code to illustrate the difference by puncturing and shortening with respect to the last coordinate.
	www-rohan.sdsu.edu /~mosulliv/Courses/UCoding01/3assign.html (173 words)

	Construction of Codes
		Given a k x n matrix A over the ring R, construct the linear code generated by the rows of A. Note that it is not assumed that the rank of A is k.
		We define G to be a permutation group of degree 7 and construct the code C as the F_2-code generated by applying the permutations of G to a certain vector:
		Given a ring R and positive integer n, return the [n, 0, n] code consisting of only the zero code word, (where the minimum weight is by convention equal to n).
	www.umich.edu /~gpcc/scs/magma/text1252.htm (1105 words)

	Hotel Discount Code
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	Netflix Coupon Code (Site not responding. Last check: 2007-11-01)
		Convolutional netflix coupon code and Block Coding Introduces the family of convolutional codes, hard netflix coupon code and soft-decision Viterbi algorithms netflix coupon code and the most prominent classes of block codes, namely Reed-Solomon (RS) netflix coupon code and Bose-Chaudhuri-Hocquenghem (BCH) codes, as well as their algebraic netflix coupon code and trellis-decoding.
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	Z4.html
		This generalizes the Hamming code of length 7, the octacode and the Nordstrom-Robinson code.
		On the Apparent Duality of the Kerdock and Preparata Codes, A.
		The Ternary Golay Code, the Integers Mod 9 and the Coxeter-Todd Lattice, A.
	www.research.att.com /~njas/doc/Z4.html (650 words)

	Dodecahedral Faces of the Mathieu group of degree 12
		" The Golay code is probably the most important of all codes for both practical and theoretical reasons." ([17], pg.
		Golay (1902-1989) was a Swiss physicist known for his work in infrared spectroscopy among other things.
		Minimog: A 4x3 array whose rows are labeled 0,+,-, that construct the Golay code in such a way that both signed and unsigned hexads are easily recognized.
	www.nadn.navy.mil /MathDept/wdj/m_12.htm (3266 words)

	CiteULike: Tag codes (Site not responding. Last check: 2007-11-01)
		Parallel decoding of the [23, 12, 7] binary Golay code
		Algebraic decoding of the ternary (13,7,5) quadratic residue code
		Decoding the ternary (23, 12, 8) quadratic residue code
	www.citeulike.org /tag/codes (914 words)

	Brouwer-Haemers graph (Site not responding. Last check: 2007-11-01)
		(iv) This graph also is the coset graph of the truncated ternary Golay code.
		The stabilizer has three orbits, of sizes 15+60+6, where such orbits of size 6 are the maximal 6-cocliques.
		Such cocliques are most easily seen in the representation of ternary vectors of length 6 with sum 1, modulo the all-1 vector.
	www.win.tue.nl /~aeb/drg/graphs/Brouwer-Haemers.html (352 words)

	Asp Code
		The code examples in this book are based upon the ASP.NET Beta2 specifications, a functionally complete version of the software.
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		We conjecture that every weight class in a Type III code with the all-one codeword holds 3-colored 3-designs.
		853 The theory of error-correcting codes (context) - MacWilliams, Sloane - 1977
	citeseer.ist.psu.edu /bonnecaze99tricolore.html (492 words)

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