Generating generalized necklaces and new quasi-cyclic codes

Year 2020, Volume: 7 Issue: 3, 237 - 245, 06.09.2020

Rumen Daskalov Elena Metodıeva

https://doi.org/10.13069/jacodesmath.784999

Abstract

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).

Keywords

Finite field, Quasi-cyclic linear codes, Necklaces

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