On some constacyclic codes over Z4[ u] / 〈u2- 1 〉 , their Z4 images, and new codes


Aydin N., ÇENGELLENMİŞ Y., Dertli A.

Designs, Codes, and Cryptography, vol.86, no.6, pp.1249-1255, 2018 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 86 Issue: 6
  • Publication Date: 2018
  • Doi Number: 10.1007/s10623-017-0392-y
  • Journal Name: Designs, Codes, and Cryptography
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1249-1255
  • Keywords: Best known codes, Codes over rings, Constacyclic codes, Gray map, Quaternary codes
  • Trakya University Affiliated: Yes

Abstract

In this paper, we study λ-constacyclic codes over the ring R= Z4+ uZ4 where u2= 1 , for λ= 3 + 2 u and 2 + 3 u. Two new Gray maps from R to Z43 are defined with the goal of obtaining new linear codes over Z4. The Gray images of λ-constacyclic codes over R are determined. We then conducted a computer search and obtained many λ-constacyclic codes over R whose Z4-images have better parameters than currently best-known linear codes over Z4.