Nonexistence of [n, 5, d]q Codes Attaining the Griesmer Bound for q4 - 2q2 - 2q + 1 ≤ d ≤ q4 - 2q2 - q

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

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Abstract

We prove that there does not exist a [q4+q3驴q2驴3q驴1, 5, q4驴2q2驴2q+1]q code over the finite field $$\mathbb{F}_q$$ for q驴 5. Using this, we prove that there does not exist a [gq(5, d), 5, d]q code with q4 驴2q2 驴2q +1 驴 d 驴 q4 驴2q2 驴q for q驴 5, where gq(k,d) denotes the Griesmer bound.