Journal Article10.1109/TIT.2003.815800
Cubic self-dual binary codes
16
TL;DR: All binary codes of that type can be obtained by a cubic construction that generalizes Turyn's, and necessary conditions for the existence of a cubic Type II code are derived.
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Abstract: We study binary self-dual codes with a fixed point free automorphism of order three. All binary codes of that type can be obtained by a cubic construction that generalizes Turyn's. We regard such "cubic" codes of length 3/spl lscr/ as codes of length /spl lscr/ over the ring F/sub 2//spl times/F/sub 4/. Classical notions of Type II codes, shadow codes, and weight enumerators are adapted to that ring. Two infinite families of cubic codes are introduced. New extremal binary codes in lengths /spl les/ 66 are constructed by a randomized algorithm. Necessary conditions for the existence of a cubic [72,36,16] Type II code are derived.
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Citations
New cubic self-dual codes of length 54, 60 and 66
TL;DR: In this article, the authors studied the construction of quasi-cyclic self-dual codes, especially of binary cubic ones, and showed that there are no more binary self dual codes with length more than 54, 60 and 66.
3
•Posted Content
Some ternary cubic two-weight codes.
TL;DR: Two new infinite families of two-weight codes which are optimal are obtained and applications of the image codes to secret sharing schemes are given.
2
Construction of cubic self-dual codes
Sunghyu Han,Jon-Lark Kim,Heisook Lee,Yoonjin Lee +3 more
- 28 Jun 2009
TL;DR: A new quasi-cyclic self-dual [24, 12, 9] code over F5 is found, whose corresponding lattice by Construction A is shown to be the odd Leech lattice O24.
2
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Duality for modules over finite rings and applications to coding theory
TL;DR: In this paper, the authors set a foundation for the study of linear codes over finite Frobenius rings, which is the most appropriate for coding theoretic purposes because two classical theorems of Mac Williams, the extension theorem and the Mac Williams identities, generalize from finite fields to finite rings.
A new upper bound on the minimal distance of self-dual codes
John H. Conway,Neil J. A. Sloane +1 more
TL;DR: It is shown that the minimal distance d of a binary self-dual code of length n>or=74 is at most 2((n+6)/10).