On Hadamard matrices constructible by circulant submatrices

Author:
C. H. Yang

Journal:
Math. Comp. **25** (1971), 181-186

MSC:
Primary 05.25

DOI:
https://doi.org/10.1090/S0025-5718-1971-0288037-7

Corrigendum:
Math. Comp. **28** (1974), 1183-1184.

Corrigendum:
Math. Comp. **28** (1974), 1183-1184.

MathSciNet review:
0288037

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let be an *H*-matrix of order 2*n* constructible by using circulant submatrices. A recursive method has been found to construct by using circulant submatrices which are derived from submatrices of a given . A similar method can be applied to a given , an *H*-matrix of Williamson type with odd *n*, to construct . All constructible by the standard type, for , and some , for , are listed and classified by this method.

**[1]**L. D. Baumert and Marshall Hall Jr.,*Hadamard matrices of the Williamson type*, Math. Comp.**19**(1965), 442–447. MR**0179093**, https://doi.org/10.1090/S0025-5718-1965-0179093-2**[2]**Marshall Hall Jr.,*Combinatorial theory*, Blaisdell Publishing Co. Ginn and Co., Waltham, Mass.-Toronto, Ont.-London, 1967. MR**0224481****[3]**Herbert John Ryser,*Combinatorial mathematics*, The Carus Mathematical Monographs, No. 14, Published by The Mathematical Association of America; distributed by John Wiley and Sons, Inc., New York, 1963. MR**0150048****[4]**John Williamson,*Hadamard’s determinant theorem and the sum of four squares*, Duke Math. J.**11**(1944), 65–81. MR**0009590****[5]**C. H. Yang,*On designs of maximal (+1,-1)-matrices of order 𝑛≡2(𝑚𝑜𝑑4)*, Math. Comp.**22**(1968), 174–180. MR**0225476**, https://doi.org/10.1090/S0025-5718-1968-0225476-4**[6]**C. H. Yang,*On designs of maximal (+1,-1)-matrices of order 𝑛≡2(𝑚𝑜𝑑4). II*, Math. Comp.**23**(1969), 201–205. MR**0239748**, https://doi.org/10.1090/S0025-5718-1969-0239748-1**[7]**L. D. Baumert,*Hadamard matrices of orders 116 and 232*, Bull. Amer. Math. Soc.**72**(1966), 237. MR**0186567**, https://doi.org/10.1090/S0002-9904-1966-11481-7

Retrieve articles in *Mathematics of Computation*
with MSC:
05.25

Retrieve articles in all journals with MSC: 05.25

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1971-0288037-7

Keywords:
Construction of Hadamard matrices,
circulant matrices,
standard type *H*-matrices,
Williamson type *H*-matrices,
recursive method for *H*-matrices,
table for some *H*-matrices

Article copyright:
© Copyright 1971
American Mathematical Society