Linear codes and the existence of a reversible Hadamard difference set inZ2×Z2×Z45☆
Linear codes over GF(5) are utilized for the construction of a reversible abelian Hadamard difference set in Z2×Z2×Z45. This is the first example of an abelian Hadamard difference set in a group of order divisible by a prime p≡1 (mod 4). Applying the Turyn composition theorem, one obtains abelian difference sets and Hadamard matrices of Williamson type of order 4×54n×p4n11×…×p4ntt where n, n1, …, ntare arbitrary non-negative integers and each pi is a prime, pi≡3 (mod 4).
Journal of Combinatorial Theory, Series A
van Eupen, M.,
Linear codes and the existence of a reversible Hadamard difference set inZ2×Z2×Z45☆.
Journal of Combinatorial Theory, Series A,
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Copyright © 1997 Academic Press. All rights reserved. Publisher’s version of record: https://doi.org/10.1006/jcta.1997.2759