2022/10/21 by Hongwei Liu, Shengwei Liu, Liu, Hongwei +1 · 1 citation
Computer Science · Engineering · #Advanced Wireless Network Optimization #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Computer and information sciences #Information Theory (cs.IT)
paper · pdf · doi:10.48550/arxiv.2210.11966
openalex publication_date 2022/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Maximum distance separable (MDS) codes are optimal in the sense that the minimum distance cannot be improved for a given length and code size. The most prominent MDS codes are generalized Reed-Solomon (GRS) codes. The square C2 of a linear code C is the linear code spanned by the component-wise products of every pair of codewords in C. For an MDS code C, it is convenient to determine whether C is a GRS code by determining the dimension of C2. In this paper, we investigate under what conditions that MDS constacyclic codes are GRS. For this purpose, we first study the square of constacyclic codes. Then, we give a sufficient condition that a constacyclic code is GRS. In particular, We provide a necessary and sufficient condition that a constacyclic code of a prime length is GRS.