Polyadic codes revisited

We generalize the notions of duadic codes, triadic codes, polyadic codes, and split group codes to include noncyclic Abelian codes. Necessary and sufficient conditions for the existence of such codes, and properties such as a duality property and a lower bound on the minimum weight of the subcode of "odd-like" codewords, are studied. This construction and its modification lead to many good codes, eight of which have minimum distance better than the lower bound given in Brouwer's table.