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 ℤpℤp[u] can be viewed as ℤp[u][x]-submodules of ℤp[x]/(xα − 1) × ℤp[u][x]/(xβ − 1), where ℤp[u] = ℤp + uℤp, u2 = 0. In this paper, we determine the generator polynomials and the minimal generating sets of this family of codes as ℤp[u]-submodules of ℤp[x] / (xα−1) × ℤp[u][x] / (xβ−1). Further, we also determine the generator polynomials of the dual codes of ℤpℤp[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.
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: 15 May 2018 *