A weighted version of a result of Hamada on minihypers and on linear codes meeting the Griesmer bound

Authors:
I. Landjev;L. Storme
Affiliations:
New Bulgarian University, Sofia, Bulgaria 1618 and Institute of Mathematics and Informatics, BAS, Sofia, Bulgaria 1113;Department of Pure Mathematics and Computer Algebra, Ghent University, Ghent, Belgium 9000
Venue:
Designs, Codes and Cryptography
Year:
2007

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Abstract

Minihypers were introduced by Hamada to investigate linear codes meeting the Griesmer bound. Hamada (Bull Osaka Women's Univ 24:1---47, 1985; Discrete Math 116:229---268, 1993) characterized the non-weighted minihypers having parameters , with k-1 λ1 λ2 ... λh ≥ 0, as the union of a λ1-dimensional space, λ2-dimensional space, …, λh-dimensional space, which all are pairwise disjoint. We present in this article a weighted version of this result. We prove that a weighted -minihyper , with k-1 λ1 λ2 … λh ≥ 0, is a sum of a λ1-dimensional space, λ2-dimensional space, …, and λh-dimensional space.