Self-Dual Cyclic and Quantum Codes Over Z2^{\alpha} x (Z2 + uZ2)^{\beta}
Information Theory
2017-11-10 v1 math.IT
Abstract
In this paper we introduce self-dual cyclic and quantum codes over Z2^{\alpha} x (Z2 + uZ2)^{\beta}. We determine the conditions for any Z2Z2[u]-cyclic code to be self-dual, that is, C = C^{\perp}. Since the binary image of a self-orthogonal Z2Z2[u]-linear code is also a self-orthogonal binary linear code, we introduce quantum codes over Z2^{\alpha} x (Z2 + uZ2)^{\beta}. Finally, we present some examples of self-dual cyclic and quantum codes that have good parameters.
Keywords
Cite
@article{arxiv.1711.03307,
title = {Self-Dual Cyclic and Quantum Codes Over Z2^{\alpha} x (Z2 + uZ2)^{\beta}},
author = {Ismail Aydogdu and Taher Abualrub},
journal= {arXiv preprint arXiv:1711.03307},
year = {2017}
}