New Results and Bounds on codes over GF(17)

Eric Chen; Nuh Aydin; Fredrik  Jönsson; Kamilla  Klonowska

doi:10.13069/jacodesmath.v11i1.257

Eric Chen Kristianstad University
Nuh Aydin Kenyon College
Fredrik Jönsson
Kamilla Klonowska

DOI: https://doi.org/10.13069/jacodesmath.v11i1.257

Keywords: quasi-cyclic codes, quasi-twisted codes, search algorithms for linear codes, distance bounds, lower bounds, upper bounds, optimal codes

Abstract

Determining the best possible values of the parameters of a linear code is one of the most fundamental and challenging problems in coding theory. There exist databases of best-known linear codes (BKLC) over small finite fields. In this work, we establish a database of BKLCs over the field GF(17) together with upper bounds on the minimum distances for lengths up to 150 and dimensions up to 6. In the process, we have found many new linear codes over GF(17).