Optimal linear rate 12 codes over F5 and F7
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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Let $n_q(k,d)$ denote the smallest value of $n$ for which there exists a linear $[n,k,d]$-code over the Galois field $GF(q)$. An $[n,k,d]$-code whose length is equal to $n_q(k,d)$ is called {em optimal}. In this paper we present some matrix generators for the family of optimal $[n,3,d]$ codes over $GF(7)$ and $GF(11)$. Most of our given codes in $GF(7)$ are non-isomorphic with the codes pre...
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one of the most important problems of coding theory is to construct codes with beat possible minimum distances. In this paper, we use the algebraic structure of quasi-cyclic codes and the BCH type bound on the minimum distance to search for quasi-cyclic codes over IFS, the finite field with five elements, which improve the minimum distances of best-known linear codes. We construct 15 new linear...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2003
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(02)00622-2