Generating generalized necklaces and new quasi-cyclic codes

• Main Authors: Rumen Daskalov, Elena Metodıeva
• Format: Article
• Language: English
• Published: Yildiz Technical University 2020-09-01
• Series: Journal of Algebra Combinatorics Discrete Structures and Applications
• Subjects: finite field; quasi-cyclic linear codes; necklaces
• Online Access: https://dergipark.org.tr/tr/pub/jacodesmath/issue/56695/784999?publisher=yildiz

In many cases there is a need of exhaustive lists of combinatorial objects of a given type. We consider generation of all inequivalent polynomials from which defining polynomials for constructing quasi-cyclic (QC) codes are to be chosen. Using these defining polynomials we construct 34 new good QC codes over GF(11) and 36 such codes over GF(13). In many cases there is a need of exhaustive lists of combinatorial objects of a given type. We consider generation of all inequivalent polynomials from which defining polynomials for constructing quasi-cyclic (QC) codes are to be chosen. Using these defining polynomials we construct 34 new good QC codes over GF(11) and 36 such codes over GF(13).