Gray Images of Cyclic Codes over $\mathbb{Z}_{p^2}$ and $\mathbb{Z}_p\mathbb{Z}_{p^2}
Information Theory
2022-10-24 v2 Cryptography and Security
math.IT
Abstract
In the paper, we firstly study the algebraic structures of -additive cyclic codes and give the generator polynomials and the minimal spanning set of these codes. Secondly, a necessary and sufficient condition for a class of -additive codes whose Gray images are linear (not necessarily cyclic) over is given. Moreover, as for some special families of cyclic codes over and , the linearity of the Gray images is determined.
Keywords
Cite
@article{arxiv.2206.13810,
title = {Gray Images of Cyclic Codes over $\mathbb{Z}_{p^2}$ and $\mathbb{Z}_p\mathbb{Z}_{p^2}},
author = {Minjia Shi and Xuan Wang},
journal= {arXiv preprint arXiv:2206.13810},
year = {2022}
}