On generalized Hadamard matrices of minimum rank

Authors:
Vladimir D. Tonchev
Affiliations:
Department of Mathematical Sciences, Michigan Technological University, Houghton, MI 49931, USA
Venue:
Finite Fields and Their Applications
Year:
2004

Citing 3
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Abstract

Generalized Hadamard matrices of order q^n^-^1 (q-a prime power, n=2) over GF(q) are related to symmetric nets in affine 2-(q^n,q^n^-^1,(q^n^-^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).