On the ranks of Toeplitz matrices over finite fields Original Research Article

Let T be a skew-symmetric Toeplitz matrix with entries in a finite field. For all positive integers n let Tn be the upper n×n corner of T, with nullity νn=ν(Tn). The sequence image satisfies a unimodality property and is eventually periodic if the entries of T satisfy a periodicity condition. We compute the maximum value and the period of the nullity sequence for Toeplitz matrices of finite bandwidth. This sequence satisfies a certain symmetry condition about its maximal values. These results apply to give some information about the ranks of general skew-symmetric Toeplitz matrices with eventually periodic entries.