New Results and Bounds on codes over GF(17)

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).