matrices

*To*: mathgroup at yoda.physics.unc.edu*Subject*: matrices*From*: Count Dracula <lk3a at kelvin.seas.virginia.edu>*Date*: Sun, 19 Sep 1993 21:17:00 -0400

I started writing a Mathematica program for constructing Hadamard matrices, and got as far as matrices of order 2^k ( q + 1 ) where q is a prime (or q = 0) and k is a nonnegative integer. For orders up to 400, this leaves out {52, 92, 100, 116, 156, 172, 184, 188, 232, 236, 244, 260, 268, 292, 324, 340, 344, 356, 372, 376} For some of these orders, existence is known, e.g. 52 = 2 ( 5^2 + 1 ), where q is a prime power. Similarly for 100, 244=2(11^2+1), 340, 344=7^3 + 1. There may be some entries in the list above, for which existence is still undecided. I am looking for an algorithm to construct Hadamard matrices of order m = 2^k ( p^n + 1) where p is a prime n > 1, k >= 0 and Mod[m, 4]=0. Existence is known for these orders (Paley, 1944). I am also looking for construction methods for other orders such as 92, 116, etc. listed above. I would appreciate hearing from people who know about these constructions. Levent lk3a at kelvin.seas.virginia.edu