Filomat 2014 Volume 28, Issue 5, Pages: 897-906
https://doi.org/10.2298/FIL1405897O
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Linear, cyclic and constacyclic codes over S4 = F2 + uF2 + u2F2 + u3F2
Özger Ödemiş Zeynep (Fatih University, Department of Mathematics, İstanbul, Turkey + İzmir Kâtip Çelebi University, Department of Engineering Sciences, İzmir, Turkey)
Kara Ümmü Ümare (Fatih University, Department of Mathematics, Istanbul, Turkey)
Yıldız Bahattin (Fatih University, Department of Mathematics, Istanbul, Turkey)
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.
Keywords: Finite chain rings, cyclic codes, negacyclic codes, constacyclic codes