Two new optimal ternary two-weight codes and strongly regular graphs
type: Item
instance of: scholarly article
title: Two new optimal ternary two-weight codes and strongly regular graphs
zbMATH Open document ID: 0844.05101
DOI: 10.1016/0012-365X(94)00264-J
author: T. Aaron Gulliver
published in: Discrete Mathematics
publication date: 1996-03-25T00:00:00Z
review text: Let \(C\) be a linear \(\text{GF}(q)\)-code with generator \(k\times n\) matrix \(G\), and let \(d(C)\) be the minimal (nonzero) Hamming distance of \(C\). Let \(d_q(n, k)\) be a maximal \(d(C)\) over the linear \((n, k) \text{GF}(q)\)-codes. A linear \((n, k) \text{GF}(q)\)-code \(C\) is called optimal, if \(d(C)= d_q(n, k)\) (optimal \((n, k, d(C))\) code). Quasi-cyclic codes are a generalization of cyclic codes whereby a cyclic shift of a codeword by \(p\) positions results in a codeword. In this paper optimal \((84, 6, 54)\) and \((98, 6, 63)\) quasi-cyclic two-weight codes over \(\text{GF}(3)\) are constructed by a simple greedy heuristic combinatorial optimization algorithm. As a corollary two new strongly regular graphs with parameters \((729, 168, 27, 42)\) and \((729, 196, 43, 56)\) are obtained.
Mathematics Subject Classification ID: 05E30
Mathematics Subject Classification ID: 94B15
zbMATH DE Number: 858103
zbMATH Keywords: optimal codes
zbMATH Keywords: quasi-cyclic codes
zbMATH Keywords: cyclic codes
zbMATH Keywords: cyclic shift
zbMATH Keywords: codeword
zbMATH Keywords: two-weight codes
zbMATH Keywords: strongly regular graphs
reviewed by: Alexandre A. Makhnev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 858103