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309,568
On the classification and enumeration of selfdual codes
 Journal of Combinatorial Theory, Series A
, 1975
"... codes. For each code we give the order of its group, the number of codes equivalent to it, and its weight distribution. There is a unique [24, 12, 61 selfdual code. Several theorems on the enumeration of selfdual codes are used, including formulas for the number of such codes with minimum distanc ..."
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Cited by 82 (16 self)
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codes. For each code we give the order of its group, the number of codes equivalent to it, and its weight distribution. There is a unique [24, 12, 61 selfdual code. Several theorems on the enumeration of selfdual codes are used, including formulas for the number of such codes with minimum
Note on the Biweight Enumerators of SelfDual Codes over Z_k
, 1999
"... Recently there has been interest in selfdual codes over finite rings. In this note, gfold joint weight enumerators and gfold multiweight enumerators of codes over the ring Z k of integers modulo k are introduced as a generalization of the biweight enumerators. We investigate these weight enumer ..."
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Cited by 1 (1 self)
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Recently there has been interest in selfdual codes over finite rings. In this note, gfold joint weight enumerators and gfold multiweight enumerators of codes over the ring Z k of integers modulo k are introduced as a generalization of the biweight enumerators. We investigate these weight
neous invariants for the MacWilliams–Gleason group, ” Europ. J. Comb., vol. 20, pp. 619–627, 1999.
"... algebra system. [5] R. A. Brualdi and V. Pless, “Weight enumerators of selfdual codes,” ..."
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algebra system. [5] R. A. Brualdi and V. Pless, “Weight enumerators of selfdual codes,”
The Weight Enumerator of the Code of the Projective Plane of Order 5
 Geometriae Dedicata
, 1998
"... We determine the weight enumerator of the code of the projective plane of order 5 by hand. The main tools used are a version of Gleason's theorem on the enumerators of selfdual codes and geometric descriptions of codewords of low weight. ..."
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Cited by 5 (2 self)
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We determine the weight enumerator of the code of the projective plane of order 5 by hand. The main tools used are a version of Gleason's theorem on the enumerators of selfdual codes and geometric descriptions of codewords of low weight.
Gleason’s Theorem on SelfDual Codes and Its Generalizations
, 2006
"... One of the most remarkable theorems in coding theory is Gleason’s 1970 theorem about the weight enumerators of selfdual codes. In the past 36 years there have been hundreds of papers written about generalizations and applications of this theorem to different types of codes, always on a casebycase ..."
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Cited by 1 (0 self)
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One of the most remarkable theorems in coding theory is Gleason’s 1970 theorem about the weight enumerators of selfdual codes. In the past 36 years there have been hundreds of papers written about generalizations and applications of this theorem to different types of codes, always on a case
Double Circulant Codes over Z4 and Even Unimodular Lattices
, 1997
"... With the help of some new results about weight enumerators of selfdual codes over Z4 we investigate a class of double circulant codes over Z4, one of which leads to an extremal even unimodular 40dimensional lattice. It is conjectured that there should be “Nine more constructions of the Leech latt ..."
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Cited by 7 (0 self)
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With the help of some new results about weight enumerators of selfdual codes over Z4 we investigate a class of double circulant codes over Z4, one of which leads to an extremal even unimodular 40dimensional lattice. It is conjectured that there should be “Nine more constructions of the Leech
On the Enumeration of Binary SelfDual Codes
"... We give a classification of singlyeven selfdual binary codes of length 32, by enumerating all neighbours of the known 85 doublyeven selfdual binary codes of length 32. There are 3, 210 singlyeven selfdual binary codes of length 32 up to equivalence. This agrees in number with the enumeration b ..."
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We give a classification of singlyeven selfdual binary codes of length 32, by enumerating all neighbours of the known 85 doublyeven selfdual binary codes of length 32. There are 3, 210 singlyeven selfdual binary codes of length 32 up to equivalence. This agrees in number with the enumeration
Cyclic SelfDual Codes
, 1983
"... It is shown that if the automorphism group of a binary selfdual code satisfies a certain condition then the code contains words of weight congruent to 2 modulo 4. In particular, no cyclic binary selfdual code can have all its weights divisible by 4. The number of cyclic binary selfdual codes of l ..."
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Cited by 71 (5 self)
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It is shown that if the automorphism group of a binary selfdual code satisfies a certain condition then the code contains words of weight congruent to 2 modulo 4. In particular, no cyclic binary selfdual code can have all its weights divisible by 4. The number of cyclic binary selfdual codes
Enumeration of the Binary SelfDual Codes of Length 34
 Codes Cryptogr
"... An (n, k) binary selforthogonal code is an (n, k) binary linear code C that is contained in its orthogonal complement C # . A selforthogonal code C is selfdual if C = C # . Two codes, C 1 and C 2 , are equivalent if and only if there exists a coordinate permutation of C 1 that takes C 1 into C ..."
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Cited by 17 (3 self)
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An (n, k) binary selforthogonal code is an (n, k) binary linear code C that is contained in its orthogonal complement C # . A selforthogonal code C is selfdual if C = C # . Two codes, C 1 and C 2 , are equivalent if and only if there exists a coordinate permutation of C 1 that takes C 1
Results 1  10
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309,568