Title: pp[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 ℤpp[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 ℤpp[u]-additive cyclic codes. Moreover, some binary quantum codes are constructed by additive cyclic codes over ℤ22[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: 15 May 2018 *

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