Quasi-Twisted Codes over \(F_{11}\)

Abstract

Let \(d_{q}(n,k)\) be the maximum possible minimum Hamming distance of a linear \([n, k]\) code over \(\mathbb{F}_q\). Tables of best known linear codes exist for all fields up to \(q = 9\). In this paper, linear codes over \(\mathbb{F}_{11}\) are constructed for \(k\) up to \(7\). The codes constructed are from the class of quasi-twisted codes. These results show that there exists a \((78,8)\) arc in \(\text{PG}(2,11)\). In addition, the minimum distances of the extended quadratic residue codes of lengths \(76\), \(88\) and \(108\) are determined.