Back to Search
Start Over
A class of constacyclic codes are generalized Reed–Solomon codes.
- Source :
- Designs, Codes & Cryptography; Dec2023, Vol. 91 Issue 12, p4143-4151, 9p
- Publication Year :
- 2023
-
Abstract
- 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 C 2 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 C 2 . 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- REED-Solomon codes
LINEAR codes
Subjects
Details
- Language :
- English
- ISSN :
- 09251022
- Volume :
- 91
- Issue :
- 12
- Database :
- Complementary Index
- Journal :
- Designs, Codes & Cryptography
- Publication Type :
- Academic Journal
- Accession number :
- 173432035
- Full Text :
- https://doi.org/10.1007/s10623-023-01294-6