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ℤ4R-additive cyclic and constacyclic codes and MDSS codes.
- Source :
-
Discrete Mathematics, Algorithms & Applications . Jan2023, Vol. 15 Issue 1, p1-21. 21p. - Publication Year :
- 2023
-
Abstract
- In this paper, we will study the structure of ℤ 4 R -additive codes where ℤ 4 = { 0 , 1 , 2 , 3 } is the well-known ring of 4 elements and R is the ring given by R = ℤ 4 + u ℤ 4 + v ℤ 4 , where u 2 = u , v 2 = v and u v = v u = 0. We will classify all maximum distance separable codes with respect to the Singleton bound (MDSS) over ℤ 4 R. Then we will focus on ℤ 4 R -additive cyclic and constacyclic codes. We will find a unique set of generator polynomials for these codes and determine minimum spanning sets for them. We will also find the generator polynomials for the dual of any ℤ 4 R -additive cyclic or constacyclic code. [ABSTRACT FROM AUTHOR]
- Subjects :
- *CYCLIC codes
*CODE generators
Subjects
Details
- Language :
- English
- ISSN :
- 17938309
- Volume :
- 15
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Discrete Mathematics, Algorithms & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 161657302
- Full Text :
- https://doi.org/10.1142/S1793830922500665