IDENTIFYING CYCLIC AND (1 + 2 ????)-CONSTACYCLIC CODES OVER ℤ4[????]/⟨ ????3 - 1⟩ WITH ℤ4 - LINEAR CODES

IDENTIFYING CYCLIC AND (1 + 2 ????)-CONSTACYCLIC CODES OVER ℤ4[????]/⟨ ????3 - 1⟩ WITH ℤ4 - LINEAR CODES

ST T. Kom, O. R. Devi

[PDF]

Abstract

This paper studies cyclic and (1 + 2v)-constacyclic codes over the ring Z4[v]/⟨v3 − 1⟩. By introducing three different Gray maps, we show that the Gray images of cyclic codes are quasi-cyclic codes over Z4 and that of (1 + 2v)-constacyclic codes are cyclic, quasi-cyclic and permutation equivalent to quasi-cyclic codes over Z4. Moreover, we show that the Gray image of skew (1 + 2v)-constacyclic code is a quasi-cyclic code over Z4.

Keywords

Cyclic code, Gray map, constacyclic code, quasi-cyclic code, skew consta- cyclic code.