منابع مشابه
Optimal Linear Codes over Z
We examine the main linear coding theory problem and study the structure of optimal linear codes over the ring Zm. We derive bounds on the maximum Hamming weight of these codes. We give bounds on the best linear codes over Z8 and Z9 of lengths up to 6. We determine the minimum distances of optimal linear codes over Z4 for lengths up to 7. Some examples of optimal codes are given.
متن کاملCYCLIC CODES AND THEIR DUALS OVER Zm
In this paper we study the cyclic codes over Zm as being Zm-submodules of ZmG and we find their minimal generating sets. We also study the dual codes of cyclic codes and find their generators as being ideals in ZmG. Throughout this paper, we assume m = q, q is a prime number and (n, q) = 1.
متن کاملOptimal Linear Codes Over GF(7) and GF(11) with Dimension 3
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...
متن کاملOn 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...
متن کاملA generalized DFT for Abelian codes over Zm
r,-/r i+1 , and N D (Cj) is the complexity of the algorithm used in the soft-decision ML decoding of C L. Therefore, the overall complexity (normalized to two dimensions) of the generalized multistage decoding algorithm can then be estimated by b ~ i 7V D (A ;) + b. (3) From Theorem 5, and (l)-(3), we are able to determine the performance and the complexity of the proposed algorithm in the deco...
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ژورنال
عنوان ژورنال: Journal of the Korean Mathematical Society
سال: 2007
ISSN: 0304-9914
DOI: 10.4134/jkms.2007.44.5.1139