Split group codes

We construct a class of codes of length n such that the minimum distance d outside of a certain subcode is, up to a constant factor, bounded below by the square root of n, a well-known property of quadratic residue codes. The construction, using the group algebra of an Abelian group and a special partition or splitting of the group, yields quadratic residue codes, duadic codes, and their generalizations as special cases. We show that most of the special properties of these codes have analogues for split group codes, and present examples of new classes of codes obtained by this construction.