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On the Minimum Length of some Linear Codes of Dimension 5

Authors:	E J Cheon T Kato S J Kim

Institution:	(1) Department of Mathematics, Gyeongsang National University, Jinju, 660-701, Korea;(2) Department of Mathematical Sciences, Yamaguchi University, Yamaguchi 753-8512, Japan;(3) Department of Mathematics and RINS, Gyeongsang National University, Jinju, 660-701, Korea

Abstract:	In this paper, we shall prove that the minimum length n_q(5,d) is equal to g_q(5,d) +1 for q⁴−2q²−2q+1≤ d≤ q⁴ − 2q² − q and 2q⁴ − 2q³ − q² − 2q+1 ≤ d ≤ 2q⁴−2q³−q²−q, where g_q(5,d) means the Griesmer bound ${\sum_{i = 0}^{4}} \lceil {\frac{d}{q^{i}}}\rceil$ . Communicated by: J.D. Key

Keywords:	Griesmer bound linear code projective space
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