Symmetric Weighing Matrices Constructed using Group Matrices

Authors:
Miin Huey Ang;Siu Lun Ma
Affiliations:
Pusat Pengajian Sains Matematik, Universiti Sains Malaysia, Penang, Malaysia 11800;Department of Mathematics, National University of Singapore, Singapore, Republic of Singapore 119260
Venue:
Designs, Codes and Cryptography
Year:
2005

Citing 4
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Abstract

A weighing matrix of order n and weight m2 is a square matrix M of order n with entries from {-1,0,+1} such that MMT=m2I where I is the identity matrix of order n. If M is a group matrix constructed using a group of order n, M is called a group weighing matrix. Recently, group weighing matrices were studied intensively, especially when the groups are cyclic and abelian. In this paper, we study the abelian group weighing matrices that are symmetric, i.e.MT=M. Some new examples are found. Also we obtain a few exponent bounds on abelian groups that admit symmetric group weighing matrices. In particular, we prove that there is no symmetric abelian group weighing matrices of order 2pr and weight p2 where p is a prime and p驴 5.