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A database of linear codes over F 13 with minimum distance bounds and new quasi-twisted codes from a heuristic search algorithm Abstract: Error control codes have been widely used in data communications and storage systems. One central problem in coding theory is to optimize the parameters of a linear code and construct codes with best possible parameters. There are tables of best-known linear codes over finite fields of sizes up to 9. Recently, there has been a growing interest in codes over F13 and other fields of size greater than 9. The main purpose of this work is to present a database of best-known linear codes over the field F13 together with upper bounds on the minimum distances. To find good linear codes to establish lower bounds on minimum distances, an iterative heuristic computer search algorithm is employed to construct quasi-twisted (QT) codes over the field F13 with high minimum distances. A large number of new linear codes have been found, improving previously best-known results. Tables of [pm, m] QT codes over F13 with best-known minimum distances as well as a table of lower and upper bounds on the minimum distances for linear codes of length up to 150 and dimension up to 6 are presented.2010 MSC: 94B05, 94B65

One fundamental and challenging problem in coding theory is to optimize the parameters [n, k, d] of a linear code over the finite field Fq and construct codes with best possible parameters. There are tables and databases of best-known linear codes over the finite fields of size up to 9 together with upper bounds on the minimum distances. Motivated by recent works on codes over F 11 , we present a table of best-known linear codes over F 11 together with upper bounds on minimum distances. Our table covers the range n ≤ 150 for the length, and 3 ≤ k ≤ 7 for the dimension. To the best of our knowledge, this is the first time such a table is presented in the literature. For the construction of the best-known codes, we employed an iterative heuristic search algorithm to search for new linear codes in the class of quasi-twisted (QT) codes. The search yielded many new codes with better parameters than previously known codes. In many cases, optimal codes are obtained. In addition to presenting a comprehensive table of best-known codes over F 11 of dimensions up to 7 with upper bounds on the minimum distances, we also present separate tables for the optimal codes and new QT codes over F 11 . We hope that this work will be a useful source for further study on codes over F 11 .

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