Open AccessLinear, cyclic and constacyclic codes over S4 = F2 + uF2 + u2F2 + u3F2
Author(s) -
Ödemiş Zeynep Özger,
Ümmü Ümare Kara,
Bahattin Yıldız
Publication year - 2014
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1405897o
Subject(s) - mathematics , ring (chemistry) , binary number , linear code , discrete mathematics , combinatorics , weight distribution , block code , algorithm , arithmetic , physics , decoding methods , chemistry , organic chemistry , thermodynamics
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.