Circulant 16-modular Hadamard matrices and Jacobi sums

[摘要] We are concerned here with the existence problem of 16-niodular circulant Hadamard matrices H of size 41) (p prime), satisfying the additional condition that any two rows at distance n/2 in H are strictly orthogonal. A necessary existence condition is p drop 1 mod 8. For p drop 1 mod 16, existence follows from the more general result of a previous paper of ours, showing the existence of (p - 1)-modular matrices of the above kind. In the remaining case p drop 9 mod 16, we construct explicit examples which solve the problem whenever 2 is a fourth power modp. When 2 is not a fourth power modp, we conjecture that such matrices cannot exist. (C) 2002 Elsevier Science (USA).

[发布日期] 2002-10-01