Title: ℤ_pℤ_p[u]-additive cyclic codes

Authors: Lingyu Diao; Jian Gao

Addresses: School of Mathematics and Statistics, Shandong University of Technology, Zibo, 255000, China ' School of Mathematics and Statistics, Shandong University of Technology, Zibo, 255000, China

Abstract: Additive cyclic codes of length (α,β) over ℤ_pℤ_p[u] can be viewed as ℤ_p[u][x]-submodules of ℤ_p[x]/(x^α − 1) × ℤ_p[u][x]/(x^β − 1), where ℤ_p[u] = ℤ_p + uℤ_p, u² = 0. In this paper, we determine the generator polynomials and the minimal generating sets of this family of codes as ℤ_p[u]-submodules of ℤ_p[x] / (x^α−1) × ℤ_p[u][x] / (x^β−1). Further, we also determine the generator polynomials of the dual codes of ℤ_pℤ_p[u]-additive cyclic codes. Moreover, some binary quantum codes are constructed by additive cyclic codes over ℤ₂ℤ₂[u].

Keywords: additive cyclic codes; minimal generating sets; binary quantum codes.

DOI: 10.1504/IJICOT.2018.091815

International Journal of Information and Coding Theory, 2018 Vol.5 No.1, pp.1 - 17

Received: 19 Jun 2017
Accepted: 25 Jun 2017
Published online: 18 May 2018 *