A New Family of Amicable Hadamard Matrices
We study constructions for amicable Hadamard matrices. The family for orders 2t, t a positive integer, is explicitly exhibited. We also show that there are amicable Hadamard matrices of order (2t - 1)r + 1 for any odd integer r > 1. Now we have orders 15r + 1, 63r + 1, 255r + 1, 511r + 1, …, r > 1 an odd integer, for the first time.
KeywordsHadamard matrices Amicable Hadamard matrices Amicable Hadamard cores
AMS Subject ClassificationPrimary 05B20
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- Belevitch, V. 1950. Theory of 2n-terminal networks with applications to conference telephony, Electr. Commun., 27(3), 231–244.Google Scholar
- Seberry, J., and M. Yamada. 1992. Hadamard matrices, sequences, and block designs. In Contemporary design theory: A collection of surveys, ed. J. H. Dinitz and D. R. Stinson, 431–560. New York, NY, John Wiley and Sons.Google Scholar
- Seberry Wallis, J. 1971. Combinatorial matrices. Ph.D. Thesis, La Trobe University, Melbourne, Australia.Google Scholar
- Seberry Wallis, J. 1972. Hadamard matrices. In W. D. Wallis, Anne Penfold Street and Jennifer Seberry Wallis, Combinatorics: Room squares, sum-free sets and Hadamard matrices, ed. W. D. Wallis, A. P. Street, and J. Seberry Wallis, Lecture Notes in Mathematics, 128; 273–490. Springer Verlag, Berlin.MATHGoogle Scholar