Some Constacyclic Codes over Z(4)[u]/< u(2)>, New Gray Maps, and New Quaternary Codes

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ÇENGELLENMİŞ Y., Dertli A., Aydin N.

ALGEBRA COLLOQUIUM, vol.25, no.3, pp.369-376, 2018 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 25 Issue: 3
• Publication Date: 2018
• Doi Number: 10.1142/s1005386718000263
• Journal Name: ALGEBRA COLLOQUIUM
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Page Numbers: pp.369-376
• Keywords: constacyclic codes, codes over rings, quaternary codes, Gray maps
• Ondokuz Mayıs University Affiliated: Yes

Abstract

this paper, we study lambda-constacyclic codes over the ring R = Z(4) + uZ(4), where u(2) = 0, for lambda = 1 + 3u and 3 + u. We introduce two new Gray maps from R to Z(4)(4) and show that the Gray images of lambda-constacyclic codes over R are quasi-cyclic over Z(4). Moreover, we present many examples of lambda-constacyclic codes over R whose Z(4)-images have better parameters than the currently best-known linear codes over Z(4).