arXiv · 1703.00761
On a class of constacyclic codes over the non-principal ideal ring $\mathbb{Z}_{p^s}+u\mathbb{Z}_{p^s}$
Abstract
$(1+pw)$-constacyclic codes of arbitrary length over the non-principal ideal ring $\mathbb{Z}_{p^s} +u\mathbb{Z}_{p^s}$ are studied, where $p$ is a prime, $w\in \mathbb{Z}_{p^s}^{\times}$ and $s$ an integer satisfying $s\geq 2$. First, the structure of any $(1+pw)$-constacyclic code over $\mathbb{Z}_{p^s} +u\mathbb{Z}_{p^s}$ are presented. Then enumerations for the number of all codes and the number of codewords in each code, and the structure of dual codes for these codes are given, respectively. Then self-dual $(1+2w)$-constacyclic codes over $\mathbb{Z}_{2^s} +u\mathbb{Z}_{2^s}$ are investigated, where $w=2^{s-2}-1$ or $2^{s-1}-1$ if $s\geq 3$, and $w=1$ if $s=2$.
Explore related subjects
Keep this discovery
Yuan Cao, Yonglin Cao. 2017-03-02. On a class of constacyclic codes over the non-principal ideal ring $\mathbb{Z}_{p^s}+u\mathbb{Z}_{p^s}$. https://arxiv.org/abs/1703.00761
Cite the original work for its findings. Save a collection to share your selection of sources.