New Results and Bounds on Codes over GF(19)

Saurav Pandey; Nuh Aydin; Eric  Chen; Fredrik  Fredrik Jönsson; Kamilla  Klonowska

doi:10.13069/jacodesmath.v12i3.361

Saurav Raj Pandey University of North Carolina-Chapel Hill
Nuh Aydin Kenyon College
Eric Zhi Chen Kristianstad University
Fredrik Fredrik Jönsson Kristianstad University
Kamilla Klonowska Kristianstad University

DOI: https://doi.org/10.13069/jacodesmath.v12i3.361

Keywords: quasi-cyclic codes, best-known codes, optimal codes, GF(19)

Abstract

Explicit construction of linear codes over finite fields is one of the most important and challenging problems in coding theory. Due to the centrality of this problem, databases of best-known linear codes (BKLCs) over small finite fields have been available. Recently, new databases for BKLCs over larger alphabets have been introduced. In this work, a new database of BKLCs over the field GF(19) is introduced, containing lower and upper bounds on the minimum distances for codes with lengths up to 150 and dimensions between 3 and 6. Computer searches were conducted on cyclic, constacyclic, quasi-cyclic, and quasi-twisted codes to establish lower bounds. These searches resulted in many new linear codes over GF(19).