Some Constacyclic Codes over Z4 [u]/(u2), New Gray Maps, and New Quaternary Codes

Abstract

In this paper, we study λ-constacyclic codes over the ring R = Z<inf>4</inf> + uZ<inf>4</inf>, where u2 = 0, for λ =1 + 3u and 3 + u. We introduce two new Gray maps from R to Z<inf>4</inf> 4 and show that the Gray images of λ-constacyclic codes over R are quasi-cyclic over Z<inf>4</inf>. Moreover, we present many examples of λ-constacyclic codes over R whose Z<inf>4</inf>-images have better parameters than the currently best-known linear codes over Z<inf>4</inf>. © 2018 Academy of Mathematics and Systems Science, Chinese Academy of Sciences.