Minimum distance bounds for linear codes over  GF(11)

Rumen    Daskalov

doi:10.13069/jacodesmath.v13i1.368

Rumen Daskalov Department of mathematics, Technical University of Gabrovo

DOI: https://doi.org/10.13069/jacodesmath.v13i1.368

Keywords: Linear codes, Quasi-cyclic codes, Minimum distance bounds

Abstract

Let $[n,k,d]_q$ code be a linear code of length $n$, dimension $k$ and minimum Hamming distance $d$ over $GF(q)$. One of the most important problems in coding theory is to construct codes with best possible minimum distances. In this paper 36 new cyclic and quasi-cyclic (QC) codes over GF(11) are presented and the table from [4] is enlarged by adding three new dimensions.