On GMW designs and a conjecture of Assmus and Key

摘要

We show that a family of cyclic Hadamard designs defined from regular ovals is a sub-family of a class of difference set designs due to B. Gordon, W. H. Mills and L. R. Welch [Can. J. Math. 14 (1962), 614-625]. Using a result of R. A. Scholtz and L. R. Welch [IEEE Trans. Inform. Theory 30, No. 3 (1984), 548-553] on the linear span of GMW sequences, we give a short proof of a conjecture of Assmus and Key on the 2-rank of this family of designs. (C) 1997 Academic Press.