A class of skew-constacyclic codes over ℤ4 + uℤ4. (2017)

• Record Type: Journal Article
• Authors: Sharma, Amit; Bhaintwal, Maheshanand
• Is Part Of: International journal of information and coding theory. Volume 4:Number 4(2017)
• Page Start: 289
• Page End: 303
• Publication Date: 2017
• Subjects: Codes over &amp -- Zopf -- 4 &amp -- #43 -- u&amp -- Zopf -- 4 -- constacyclic codes -- factorisations of polynomials -- Gray map -- skew polynomial rings; Coding theory -- Periodicals; Information theory -- Periodicals; 003.54
• Languages: English
• ISSNs: 1753-7703

Abstract

In this paper, we study a class of skew-constacyclic codes over R = ℤ4 + uℤ4, which is a non-chain extension of ℤ4 . Some structural properties of R[x, θ] are discussed, where θ is an automorphism of R. We determine a necessary condition and a sufficient condition for these codes to be free, when they are principally generated. A Gray map over R is defined and some good codes are obtained using it. For even n, a relation between the generator polynomial of a code and that of its dual is obtained. Some examples are given to illustrate the results. Further, we have generalised these codes to double skew-constacyclic codes over R. Some good codes with improved minimum Lee distance over ℤ4 have been found via this class, and the same have been added to the database of ℤ4 codes.