Authors: Amit Sharma; Maheshanand Bhaintwal
Addresses: Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee 247667, India ' Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee 247667, India
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.
Keywords: Codes over ℤ4 + uℤ4; constacyclic codes; factorisations of polynomials; Gray map; skew polynomial rings.
International Journal of Information and Coding Theory, 2017 Vol.4 No.4, pp.289 - 303
Received: 09 Dec 2016
Accepted: 23 Mar 2017
Published online: 21 Jun 2017 *