A Griesmer bound for linear codes over finite quasi-Frobenius rings

Authors:
Keisuke Shiromoto;Leo Storme
Affiliations:
Department of Electronics and Informatics, Ryukoku University, Seta, Otsu 520-2194, Japan;Department of Pure Maths and Computer Algebra, Ghent University, Krijgslaan 281, 9000 Ghent, Belgium
Venue:
Discrete Applied Mathematics - Special issue: International workshop on coding and cryptography (WCC 2001)
Year:
2003

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Abstract

In this article we give a Griesmer type bound for linear codes over finite quasi-Frobenius rings and consider linear codes over these rings meeting the bound. And we study a geometrical characterization of linear codes over finite chain rings meeting the bound, that is, a one-to-one correspondence between these codes and minihypers in projective Hjelmslev spaces over these rings.