Quadratic Double Circulant Codes over Fields

A generalization of the Pless symmetry codes to different fields is presented. In particular new infinite families of self-dual codes over GF(4), GF(5), GF(7), and GF(9) are introduced. It is proven that the automorphism group of some of these codes contains the group PSL₂(q). New codes over GF(4) and GF(5), with better minimum weight than previously known codes, are given.