       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

```

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