Linear codes and the existence of a reversible Hadamard difference set inZ2×Z2×Z45☆

Authors

M. van Eupen, Michigan Technological University
Vladimir Tonchev, Michigan Technological UniversityFollow

Document Type

Article

Publication Date

5-2002

Abstract

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×…×p⁴ⁿ_tt where n, n1, …, n_tare arbitrary non-negative integers and each p_i is a prime, p_i≡3 (mod 4).

Publisher's Statement

Copyright © 1997 Academic Press. All rights reserved. Publisher’s version of record: https://doi.org/10.1006/jcta.1997.2759

Publication Title

Journal of Combinatorial Theory, Series A

Recommended Citation

van Eupen, M., & Tonchev, V. (2002). Linear codes and the existence of a reversible Hadamard difference set inZ2×Z2×Z45☆. Journal of Combinatorial Theory, Series A, 79(1), 161-167. http://doi.org/10.1006/jcta.1997.2759
Retrieved from: https://digitalcommons.mtu.edu/math-fp/150