Some constacyclic and cyclic codes over Fq[u]/〈u t+1〉

Abstract

A generalized Gray map for codes over the ring Fq〈u〉/ 〈ut+1〉 is introduced, where q = pm is a prime power. It is shown that the generalized Gray image of a linear length-N (1 - ut)-cyclic code over Fq[u]/〈ut+1〉 is a distance-invariant linear length-qtN quasi-cyclic code of index qt/p over Fq. It turns out that if (N, p) = 1 then every linear code over Fq that is the generalized Gray image of a length-N cyclic code over Fq[u]/〈ut+1〉, is also equivalent to a linear length-qtN quasi-cyclic code of index q t/p over Fq. The relationship between linear length-p N cyclic codes with (N, p) = 1 over Fp and linear length-N cyclic codes over Fp + uFp is explicitly determined. Copyright © 2010 The Institute of Electronics, Information and Communication Engineers.