Linear, cyclic and constacyclic codes over S4 = F2 + uF2 + u2F2 + u3F2-Reference-Cited by-同舟云学术

Linear, cyclic and constacyclic codes over S4 = F2 + uF2 + u2F2 + u3F2

Published:2014 Issue:5 Volume:28 Page:897-906
ISSN:0354-5180
Container-title:Filomat
language:en
Short-container-title:Filomat

Author:

Özger Ödemiş¹,Kara Ümmü²,Yıldız Bahattin²

Affiliation:

1. Fatih University, Department of Mathematics, İstanbul, Turkey + İzmir Kâtip Çelebi University, Department of Engineering Sciences, İzmir, Turkey

2. Fatih University, Department of Mathematics, Istanbul, Turkey

Abstract

In this work, linear codes over the ring S4 = F2 + uF2 + u2F2 + u3F2 are considered. The Lee weight and gray map for codes over S4 are defined and MacWilliams identities for the complete, the symmetrized and the Lee weight enumerators are obtained. Cyclic and (1 + u2)-constacyclic codes over S4 are studied, as a result of which a substantial number of optimal binary codes of different lengths are obtained as the Gray images of cyclic and constacyclic codes over S4.

Publisher

National Library of Serbia

Subject

General Mathematics

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