A new extension theorem for 3-weight modulo q linear codes over $${\mathbb{F}_ q}$$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

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A new extension theorem for 3-weight modulo q linear codes over $${\mathbb{F}_ q}$$

Authors:	E J Cheon T Maruta

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

Abstract:	We prove that every n, k, d]_q code with q ≥ 4, k ≥ 3, whose weights are congruent to 0, −1 or −2 modulo q and ${d \equiv -1 \pmod{q}}$ is extendable unless its diversity is ${\left({q \choose 2}q^{k-3}+\theta_{k-3}, {q\choose 2}q^{k-3}\right)}$ for odd q, where ${\theta_j = (q^{j+1}-1)/(q-1)}$ .

Keywords:	Extension theorem Linear code 3-weight Projective space
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