On weights in duadic abelian codes

In this note, we prove that if C is a duadic binary abelian code with splitting mu = mu-1 and the minimum odd weight of C satisfies d(2) - d + 1 not equal n, then d(d - 1) > n + 11. We show by an example that this bound is sharp. A series of open problems on this subject are proposed, (C) 2002 Elsevier Science B.V. All rights reserved.