On the minimum length of some linear codes期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

On the minimum length of some linear codes

Authors:	E J Cheon T Maruta

Institution:	(1) Department of Mathematics, Gyeongsang National University, Jinju, 660-701, Korea;(2) Department of Mathematics and Information Sciences, Osaka Prefecture University, Sakai, Osaka 599-8531, Japan

Abstract:	We determine the minimum length n _q (k, d) for some linear codes with k ≥ 5 and q ≥ 3. We prove that n _q (k, d) = g _q (k, d) + 1 for $q^{k-1}-2q^{\frac{k-1}{2}}-q+1 \le d \le q^{k-1}-2q^{\frac{k-1}{2}}$ when k is odd, for $q^{k-1}-q^{\frac{k}{2}}-q^{{\frac{k}{2}}-1} -q+1 \le d \le q^{k-1}-q^{\frac{k}{2}}-q^{{\frac{k}{2}}-1}$ when k is even, and for $2q^{k-1}-2q^{k-2}-q^2-q+1 \le d \le 2q^{k-1}-2q^{k-2}-q^2$ . This work was supported by the Korea Research Foundation Grant funded by the Korean Government(MOEHRD). (KRF-2005-214-C00175). This research has been partially supported by Grant-in-Aid for Scientific Research of Japan Society for the Promotion of Science under Contract Number 17540129.

Keywords:	Griesmer bound Linear code 0-Cycle Minimum length Minihypers Projective space
本文献已被 SpringerLink 等数据库收录！