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Masaaki Harada - One of the best experts on this subject based on the ideXlab platform.
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on a 5 design related to a putative extremal doubly even self dual Code of length a multiple of 24
arXiv: Combinatorics, 2014Co-Authors: Masaaki HaradaAbstract:By the Assmus and Mattson theorem, the Codewords of each nontrivial weight in an extremal doubly even Self-Dual Code of length 24m form a self-orthogonal 5-design. In this paper, we study the Codes constructed from self-orthogonal 5-designs with the same parameters as the above 5-designs. We give some parameters of a self-orthogonal 5-design whose existence is equivalent to that of an extremal doubly even Self-Dual Code of length 24m for m=3,...,6. If $m \in \{1,\ldots,6\}$, $k \in \{m+1,\ldots,5m-1\}$ and $(m,k) \ne (6,18)$, then it is shown that an extremal doubly even Self-Dual Code of length 24m is generated by Codewords of weight 4k.
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an extremal doubly even self dual Code of length 112
Electronic Journal of Combinatorics, 2008Co-Authors: Masaaki HaradaAbstract:In this note, an extremal doubly even Self-Dual Code of length $112$ is constructed for the first time. This length is the smallest length for which no extremal doubly even Self-Dual Code of length $n \not\equiv 0 \pmod{24}$ has been constructed.
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an extremal singly even self dual Code of length 88
Advances in Mathematics of Communications, 2007Co-Authors: Masaaki Harada, Takuji NishimuraAbstract:An extremal singly even Self-Dual [88, 44, 16] Code is constructed for the first time. Some optimal (extremal) singly even Self-Dual Codes with weight enumerators which were not known to be attainable are also found for lengths 68 and 92.
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a characterization of designs related to an extremal doubly even self dual Code of length 48
Annals of Combinatorics, 2005Co-Authors: Masaaki Harada, Akihiro Munemasa, Vladimir D TonchevAbstract:The uniqueness of a binary doubly-even Self-Dual [48, 24, 12] Code is used to prove that a self-orthogonal 5-(48, 12, 8) design, as well as some of its derived and residual designs, including a quasi-symmetric 2-(45, 9, 8) design, are all unique up to isomorphism.
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on a 5 design related to an extremal doubly even self dual Code of length 72
Journal of Combinatorial Theory Series A, 2004Co-Authors: Masaaki Harada, Masaaki Kitazume, Akihiro MunemasaAbstract: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.
Chaoping Xing - One of the best experts on this subject based on the ideXlab platform.
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new mds self dual Codes from generalized reed solomon Codes
IEEE Transactions on Information Theory, 2017Co-Authors: Lingfei Jin, Chaoping XingAbstract:Both Maximum Distance Separable and Euclidean Self-Dual Codes have theoretical and practical importance and the study of MDS Self-Dual Codes has attracted lots of attention in recent years. In particular, determining the existence of $q$ -ary MDS Self-Dual Codes for various lengths has been investigated extensively. The problem is completely solved for the case where $q$ is even. This paper focuses on the case where $q$ is odd. We construct a few classes of new MDS Self-Dual Codes through generalized Reed–Solomon Codes. More precisely, we show that for any given even length $n$ , we have a $q$ -ary MDS Code as long as $q\equiv 1\bmod {4}$ and $q$ is sufficiently large (say $q\ge 4^{n}\times n^{2})$ . Furthermore, we prove that there exists a $q$ -ary MDS Self-Dual Code of length $n$ if $q=r^{2}$ and $n$ satisfies one of the three conditions: 1) $n\le r$ and $n$ is even; 2) $q$ is odd and $n-1$ is an odd divisor of $q-1$ ; and 3) $r\equiv 3\mod {4}$ and $n=2tr$ for any $t\le (r-1)/2$ .
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new mds self dual Codes from generalized reed solomon Codes
arXiv: Information Theory, 2016Co-Authors: Lingfei Jin, Chaoping XingAbstract:Both MDS and Euclidean Self-Dual Codes have theoretical and practical importance and the study of MDS Self-Dual Codes has attracted lots of attention in recent years. In particular, determining existence of $q$-ary MDS Self-Dual Codes for various lengths has been investigated extensively. The problem is completely solved for the case where $q$ is even. The current paper focuses on the case where $q$ is odd. We construct a few classes of new MDS Self-Dual Code through generalized Reed-Solomon Codes. More precisely, we show that for any given even length $n$ we have a $q$-ary MDS Code as long as $q\equiv1\bmod{4}$ and $q$ is sufficiently large (say $q\ge 2^n\times n^2)$. Furthermore, we prove that there exists a $q$-ary MDS Self-Dual Code of length $n$ if $q=r^2$ and $n$ satisfies one of the three conditions: (i) $n\le r$ and $n$ is even; (ii) $q$ is odd and $n-1$ is an odd divisor of $q-1$; (iii) $r\equiv3\mod{4}$ and $n=2tr$ for any $t\le (r-1)/2$.
Radinka Dontcheva - One of the best experts on this subject based on the ideXlab platform.
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doubly even self dual Code of length 96
IEEE Transactions on Information Theory, 2002Co-Authors: Radinka DontchevaAbstract:We prove that 23, 11, and 7 do not divide the order of the automorphism group of a binary [96, 48, 20] doubly-even Self-Dual Code. We construct 25 new inequivalent binary [96, 48, 16] doubly-even Self-Dual Codes via an automorphism of order 23.
Lingfei Jin - One of the best experts on this subject based on the ideXlab platform.
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new mds self dual Codes from generalized reed solomon Codes
IEEE Transactions on Information Theory, 2017Co-Authors: Lingfei Jin, Chaoping XingAbstract:Both Maximum Distance Separable and Euclidean Self-Dual Codes have theoretical and practical importance and the study of MDS Self-Dual Codes has attracted lots of attention in recent years. In particular, determining the existence of $q$ -ary MDS Self-Dual Codes for various lengths has been investigated extensively. The problem is completely solved for the case where $q$ is even. This paper focuses on the case where $q$ is odd. We construct a few classes of new MDS Self-Dual Codes through generalized Reed–Solomon Codes. More precisely, we show that for any given even length $n$ , we have a $q$ -ary MDS Code as long as $q\equiv 1\bmod {4}$ and $q$ is sufficiently large (say $q\ge 4^{n}\times n^{2})$ . Furthermore, we prove that there exists a $q$ -ary MDS Self-Dual Code of length $n$ if $q=r^{2}$ and $n$ satisfies one of the three conditions: 1) $n\le r$ and $n$ is even; 2) $q$ is odd and $n-1$ is an odd divisor of $q-1$ ; and 3) $r\equiv 3\mod {4}$ and $n=2tr$ for any $t\le (r-1)/2$ .
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new mds self dual Codes from generalized reed solomon Codes
arXiv: Information Theory, 2016Co-Authors: Lingfei Jin, Chaoping XingAbstract:Both MDS and Euclidean Self-Dual Codes have theoretical and practical importance and the study of MDS Self-Dual Codes has attracted lots of attention in recent years. In particular, determining existence of $q$-ary MDS Self-Dual Codes for various lengths has been investigated extensively. The problem is completely solved for the case where $q$ is even. The current paper focuses on the case where $q$ is odd. We construct a few classes of new MDS Self-Dual Code through generalized Reed-Solomon Codes. More precisely, we show that for any given even length $n$ we have a $q$-ary MDS Code as long as $q\equiv1\bmod{4}$ and $q$ is sufficiently large (say $q\ge 2^n\times n^2)$. Furthermore, we prove that there exists a $q$-ary MDS Self-Dual Code of length $n$ if $q=r^2$ and $n$ satisfies one of the three conditions: (i) $n\le r$ and $n$ is even; (ii) $q$ is odd and $n-1$ is an odd divisor of $q-1$; (iii) $r\equiv3\mod{4}$ and $n=2tr$ for any $t\le (r-1)/2$.
Akihiro Munemasa - One of the best experts on this subject based on the ideXlab platform.
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a characterization of designs related to an extremal doubly even self dual Code of length 48
Annals of Combinatorics, 2005Co-Authors: Masaaki Harada, Akihiro Munemasa, Vladimir D TonchevAbstract:The uniqueness of a binary doubly-even Self-Dual [48, 24, 12] Code is used to prove that a self-orthogonal 5-(48, 12, 8) design, as well as some of its derived and residual designs, including a quasi-symmetric 2-(45, 9, 8) design, are all unique up to isomorphism.
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on a 5 design related to an extremal doubly even self dual Code of length 72
Journal of Combinatorial Theory Series A, 2004Co-Authors: Masaaki Harada, Masaaki Kitazume, Akihiro MunemasaAbstract: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.
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extremal self dual 40 20 8 Codes with covering radius 7
Finite Fields and Their Applications, 2004Co-Authors: Masaaki Harada, Akihiro Munemasa, Kenichiro TanabeAbstract:We construct new extremal Self-Dual [40,20,8] Codes with covering radius 7. It is also shown that the vectors of a fixed weight in a coset of weight 4n+2 in an extremal doubly even Self-Dual Code of length 24n+16 such that the coset has no vector of weight 4n+4 form a 1-design.