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Quasi-cyclic and generalized quasi-cyclic codes and uniqueness of their generators.
- Source :
- Discrete Mathematics, Algorithms & Applications; Aug2023, Vol. 15 Issue 6, p1-10, 10p
- Publication Year :
- 2023
-
Abstract
- In this paper, we use a novel approach to describe generator polynomials of quasi-cyclic (QC) and generalized QC (GQC) codes over finite fields. Our study of QC- and GQC-codes will be general and not only restricted to one-generator codes. We prove that generator polynomials of QC-codes and GQC-codes are unique. Further, we use our results to obtain an expression for the dimensions of QC-codes and GQC-codes. As an application of our construction of these codes, we obtain many optimal linear codes over finite fields GF (2) , GF (3) , GF (4) and GF (5). [ABSTRACT FROM AUTHOR]
- Subjects :
- CODE generators
LINEAR codes
CYCLIC codes
FINITE fields
POLYNOMIALS
Subjects
Details
- Language :
- English
- ISSN :
- 17938309
- Volume :
- 15
- Issue :
- 6
- Database :
- Complementary Index
- Journal :
- Discrete Mathematics, Algorithms & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 164158487
- Full Text :
- https://doi.org/10.1142/S1793830922501452