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.