On Quadratic Double Circulant Codes over Fields

In this extended abstract, we give general results about quadratic double circulant codes, which can be seen as a generalization of the Pless Symmetry codes to different fields. In particular new infinite families of self-dual codes over GF(4) and GF(5) are presented. 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.