On the minimum length of linear codes over F5
نویسندگان
چکیده
منابع مشابه
On optimal linear codes over F5
Let nq(k, d) be the smallest integer n for which there exists an [n, k, d]q code for given q, k, d. It is known that n8(4, d) = ∑3 i=0 ⌈ d/8i ⌉ for all d ≥ 833. As a continuation of Jones et al. [Electronic J. Combinatorics 13 (2006), #R43], we determine n8(4, d) for 117 values of d with 113 ≤ d ≤ 832 and give upper and lower bounds on n8(4, d) for other d using geometric methods and some exten...
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چکیده ندارد.
15 صفحه اولOn self-dual codes over F5
The purpose of this paper is to improve the upper bounds of the minimum distances of self-dual codes over F5 for lengths 22, 26, 28, 32 − 40. In particular, we prove that there is no [22, 11, 9] self-dual code over F5, whose existence was left open in 1982. We also show that both the Hamming weight enumerator and the Lee weight enumerator of a putative [24, 12, 10] self-dual code over F5 are un...
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In this paper, we consider the minimum Hamming weight for linear codes over special finite quasi-Frobenius rings. Furthermore, we obtain minimal free $R$-submodules of a finite quasi-Frobenius ring $R$ which contain a linear code and derive the relation between their minimum Hamming weights. Finally, we suggest an algorithm that computes this weight using the Grobner basis and we show that und...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2015
ISSN: 0012-365X
DOI: 10.1016/j.disc.2015.01.010