A database of linear codes over F13 with minimum distance bounds and new quasi-twisted codes from a heuristic search algorithm

Error control codes have been widely used in data communications and storage systems. One centralproblem in coding theory is to optimize the parameters of a linear code and construct codes withbest possible parameters. There are tables of best-known linear codes over finite fields of sizes up to9. Recently, there has been a growing interest in codes over F13 and other fields of size greater than9. The main purpose of this work is to present a database of best-known linear codes over the fieldF13 together with upper bounds on the minimum distances. To find good linear codes to establishlower bounds on minimum distances, an iterative heuristic computer search algorithm is employed toconstruct quasi-twisted (QT) codes over the field F13 with high minimum distances. A large numberof new linear codes have been found, improving previously best-known results. Tables of [pm;m] QTcodes over F13 with best-known minimum distances as well as a table of lower and upper bounds onthe minimum distances for linear codes of length up to 150 and dimension up to 6 are presented.