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Computer generation of Hadamard matrices
Author(s) -
Balasubramanian K.
Publication year - 1993
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.540140513
Subject(s) - hadamard transform , matrix multiplication , multiplication (music) , hadamard matrix , hadamard code , matrix (chemical analysis) , skew , hadamard's inequality , code (set theory) , computer science , arithmetic , complex hadamard matrix , mathematics , algorithm , combinatorics , chemistry , physics , telecommunications , mathematical analysis , set (abstract data type) , chromatography , quantum mechanics , quantum , programming language
We develop a computer code that uses elegant bit‐manipulation techniques for matrix multiplication and thus facilitates exhaustive generation of Skew‐Hadamard matrices. Hadamard matrices are useful in spectroscopic applications (Hadamard transform spectroscopy) and in balanced chemical designs. Application of our code yields several Skew‐Hadamard matrices up to order 100 × 100, although the combinatorial complexity of exhaustive generation increases exponentially. Our bit‐manipulation‐based codes took 124 h of CPU time to perform 7.79344 × 10 11 matrix multiplications on an IBM RS 6000/560 system to generate all 100 × 100 matrices. This amounts to 5.7 × 10 −7 s of CPU time per matrix multiplication. © 1993 John Wiley & Sons, Inc.