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We introduce an altered version of the four circulant construction over group rings for self-dual codes. We consider this construction over the binary field, the rings and ; using groups of order 4 and 8. Through these constructions and their extensions, we find binary self-dual codes of lengths 16, 32, 48, 64 and 68, many of which are extremal. In particular, we find forty new extremal binary self-dual codes of length 68, including twelve new codes with in , which is the first instance of such a value in the literature. 相似文献
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We construct self-dual codes over small fields with q = 3, 4, 5, 7, 8, 9 of moderate length with long cycles in the automorphism group. With few exceptions, the codes achieve
or improve the known lower bounds on the minimum distance of self-dual codes.
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Vassil Yorgov 《Discrete Mathematics》2011,(16):1860
This note corrects a mistake in the previous paper where some of the codes are missing and others are repeated. All [42, 21, 8] binary self-dual with an automorphism of order 7 are enumerated. Up to equivalence their number is 29. 相似文献
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The purpose of this paper is to construct nontrivial MDS self-dual codes over Galois rings. We consider a building-up construction
of self-dual codes over Galois rings as a GF(q)-analogue of (Kim and Lee, J Combin Theory ser A, 105:79–95). We give a necessary and sufficient condition on which the building-up
construction holds. We construct MDS self-dual codes of lengths up to 8 over GR(32,2), GR(33,2) and GR(34,2), and near-MDS self-dual codes of length 10 over these rings. In a similar manner, over GR(52,2), GR(53,2) and GR(72,2), we construct MDS self-dual codes of lengths up to 10 and near-MDS self-dual codes of length 12. Furthermore, over GR(112,2) we have MDS self-dual codes of lengths up to 12.
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In this paper, we propose a mechanism on how to construct long MDS self-dual codes from short ones. These codes are special types of generalized Reed-Solomon (GRS) codes or extended generalized Reed-Solomon codes. The main tool is utilizing additive structure or multiplicative structure on finite fields. By applying this method, more MDS self-dual codes can be constructed. 相似文献
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A code is called formally self-dual if and have the same weight enumerators. There are four types of nontrivial divisible formally self-dual codes over , and . These codes are called extremal if their minimum distances achieve the Mallows-Sloane bound. S. Zhang gave possible lengths
for which extremal self-dual codes do not exist. In this paper, we define near-extremal formally self-dual (f.s.d.) codes.
With Zhang’s systematic approach, we determine possible lengths for which the four types of near-extremal formally self-dual
codes as well as the two types of near-extremal formally self-dual additive codes cannot exist. In particular, our result
on the nonexistence of near-extremal binary f.s.d. even codes of any even length n completes all the cases since only the case 8|n was dealt with by Han and Lee.
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We give methods for constructing many self-dual -codes and Type II -codes of length 2n starting from a given self-dual -code and Type II -code of length 2n, respectively. As an application, we construct extremal Type II -codes of length 24 for and extremal Type II -codes of length 32 for . We also construct new extremal Type II -codes of lengths 56 and 64. 相似文献
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Masaaki Harada 《Journal of Combinatorial Theory, Series A》2009,116(5):1063-1072
Ternary self-dual codes have been classified for lengths up to 20. At length 24, a classification of only extremal self-dual codes is known. In this paper, we give a complete classification of ternary self-dual codes of length 24 using the classification of 24-dimensional odd unimodular lattices. 相似文献