On the Minimum Length of some Linear Codes of Dimension 5

Authors:
E. J. Cheon;T. Kato;S. J. Kim
Affiliations:
Department of Mathematics, Gyeongsang National University, Jinju, Korea 660-701;Department of Mathematical Sciences, Yamaguchi University, Yamaguchi, Japan 753-8512;Department of Mathematics and RINS, Gyeongsang National University, Jinju, Korea 660-701
Venue:
Designs, Codes and Cryptography
Year:
2005

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On the minimum length of some linear codes

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Abstract

In this paper, we shall prove that the minimum length nq(5,d) is equal to gq(5,d) +1 for q4驴2q2驴2q+1驴 d驴 q4 驴 2q2 驴 q and 2q4 驴 2q3 驴 q2 驴 2q+1 驴 d 驴 2q4驴2q3驴q2驴q, where gq(5,d) means the Griesmer bound $${\sum_{i = 0}^{4}} \lceil {\frac{d}{q^{i}}}\rceil$$ .