It is known that there is a unique extremal self-dual [46, 23, 10] code, up to equivalence. In this correspondence, we give the complete coset weight distribution of the unique code.
It is known that there is a unique extremal self-dual [46, 23, 10] code, up to equivalence. In this correspondence, we give the complete coset weight distribution of the unique code.
It is shown that if there is a self-orthogonal 5-(72,16,78) design, then the rows of its block-point incidence matrix generate an extremal doubly even self-dual code of length 72. In other words, a putative extremal d...
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It is shown that if there is a self-orthogonal 5-(72,16,78) design, then the rows of its block-point incidence matrix generate an extremal doubly even self-dual code of length 72. In other words, a putative extremal doubly even self-dual code of length 72 is generated by the codewords of minimum weight. (C) 2004 Elsevier Inc. All rights reserved.
It has been proven in a series of works that the order of the automorphism group of a self-dual binary [72,36,16] code does not exceed five. Up to equivalence, we obtain a parametrization of all self-dual binary codes...
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It has been proven in a series of works that the order of the automorphism group of a self-dual binary [72,36,16] code does not exceed five. Up to equivalence, we obtain a parametrization of all self-dual binary codes of length 72 with automorphism of order four, which can be extremal. We use extensive computations in Magma and on a supercomputer to show that the automorphism group of an extremal self-dual binary code of length 72 does not have an element of order four.
We give the structures of a cyclic code over ringR = F2 ＋ uF2 ＋ u^2F2 = {0, 1,u, u^2,v, v^2,uv, v^3},where u^3 = 0, of odd length and its dualcode. For the cyclic code, necessary and sufficient conditions for the e...
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We give the structures of a cyclic code over ring
R = F2 ＋ uF2 ＋ u^2F2 = {0, 1,u, u^2,v, v^2,uv, v^3},
where u^3 = 0, of odd length and its dualcode. For the cyclic code, necessary and sufficient conditions for the existence of self-dual code are provided.
self-dual codes over F(5) exist for all even lengths. The smallest length for which the largest minimum weight among self-dual codes has not been determined is 24, and the largest minimum weight is either 9 or 10. In ...
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self-dual codes over F(5) exist for all even lengths. The smallest length for which the largest minimum weight among self-dual codes has not been determined is 24, and the largest minimum weight is either 9 or 10. In this note, we show that there exists no self-dual [24, 12, 10] code over F5, using the classification of 24-dimensional odd unimodular lattices due to Borcherds.
The existence of an extremal self-dual binary linear code of length 120 is a long-standing open problem. We continue the investigation of its automorphism group, proving that automorphisms of order 30 and 57 cannot oc...
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The existence of an extremal self-dual binary linear code of length 120 is a long-standing open problem. We continue the investigation of its automorphism group, proving that automorphisms of order 30 and 57 cannot occur. Supposing the involutions acting fixed point freely, we show that also automorphisms of order 8 cannot occur and the automorphism group is of order at most 120, with further restrictions. Finally, we present some necessary conditions for the existence of the code, based on shadow and design theory. (C) 2017 Elsevier Inc. All rights reserved.
An efficient algorithm is presented for calculating higher weight enumerators of linear codes given generator matrices. By this algorithm, the higher weight enumerators of the unique doubly-even, self-dual [48,24,12] ...
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An efficient algorithm is presented for calculating higher weight enumerators of linear codes given generator matrices. By this algorithm, the higher weight enumerators of the unique doubly-even, self-dual [48,24,12] code are calculated. The algorithm is based on a previously shown relationship between Tutte polynomials and higher weight enumerators.
We show that from every skew-type Hadamard matrix of order 4t one can obtain a series of skew-type Hadamard matrices of order 2(i+2)t, i a positive integer, whose binary linear codes are doubly even self-dual binary c...
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We show that from every skew-type Hadamard matrix of order 4t one can obtain a series of skew-type Hadamard matrices of order 2(i+2)t, i a positive integer, whose binary linear codes are doubly even self-dual binary codes of length 2(i+2)t. It is known that a doubly even self-dual binary code yields an even unimodular lattice. Hence, this construction of skew-type Hadamard matrices gives us a series of even unimodular lattices of rank 2(i+2)t, i a positive integer. Furthermore, we provide a construction of doubly even self-dual binary codes from conference graphs.
We deal with ACD (additive complementary dual) codes and cyclic codes over the mixed alphabet Z2Rk, where Rk := Z2[ y]/yk , k = 2. First, we establish a few criteria for Z2Rk -additive codes to be ACD codes. We also p...
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We deal with ACD (additive complementary dual) codes and cyclic codes over the mixed alphabet Z2Rk, where Rk := Z2[ y]/yk , k = 2. First, we establish a few criteria for Z2Rk -additive codes to be ACD codes. We also present conditions for separable codes and a class of additive codes (not necessarily separable) over Z2Rk to be ACD codes that are both necessary and sufficient. With the help of a Gray map, binary LCD codes are obtained from Z2Rk -additive codes. Moreover, we describe the generator polynomial of the dual of an additive cyclic code over Z2Rk. Finally, we construct examples of optimal binary codes as the Gray image of certain additive cyclic codes over Z2Rk.
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