On the Minimum Length of q-ary Linear Codes of Dimension Five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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On the Minimum Length of q-ary Linear Codes of Dimension Five

Authors:	TATSUYA MARUTA

Institution:	(1) Aichi Prefectural Women's Junior College, Mizuho, 467 Nagoya, Japan

Abstract:	Let $n_q \left( {k,d} \right)$ be the smallest integer n for which there exists a linear code of length n, dimension k and minimum Hamming distance d over the Galois field GF(q). In this paper we determine $n_q \left( {5,d} \right)$ for $q^4 - q^3 - q - \sqrt q - 2 < d \leqslant q^4 - q^3 + q^2 - q$ for all q, using a geometric method.

Keywords:	linear code the Griesmer bound minihyper
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