On generalized Hadamard matrices of minimum rank

Authors

Vladimir Tonchev, Michigan Technological UniversityFollow

Document Type

Article

Publication Date

10-2004

Abstract

Generalized Hadamard matrices of order qⁿ⁻¹ (q—a prime power, n⩾2) over GF(q) are related to symmetric nets in affine 2-(qⁿ,qⁿ⁻¹,(qⁿ⁻¹−1)/(q−1)) designs invariant under an elementary abelian group of order q acting semi-regularly on points and blocks. The rank of any such matrix over GF(q) is greater than or equal to n−1. It is proved that a matrix of minimum q-rank is unique up to a monomial equivalence, and the related symmetric net is a classical net in the n-dimensional affine geometry AG(n,q).

Publisher's Statement

Copyright © 2003 Elsevier Inc. All rights reserved. Publisher’s version of record: https://doi.org/10.1016/j.ffa.2003.11.001

Publication Title

Finite Fields and Their Applications

Recommended Citation

Tonchev, V. (2004). On generalized Hadamard matrices of minimum rank. Finite Fields and Their Applications, 10(4), 522-529. http://doi.org/10.1016/j.ffa.2003.11.001
Retrieved from: https://digitalcommons.mtu.edu/math-fp/121