New results and bounds on codes over $GF(17)$

Source 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 $GF(17)$. Received: 10 August 2022 | Accepted: 5 December 2022