LAUSR

Abstract For each non-negative integer n let A n be an n + 1 by n + 1 Toeplitz matrix over a finite field, F, and suppose for each n that A n is embedded in the upper left corner of A n + 1 . We study the structure of the sequence ν = { ν n : n ∈ Z + } , where ν n = null ( A n ) is the nullity of A n . For each n ∈ Z + and each nullity pattern ν 0 , ν 1 , … , ν n , we count the number of strings of Toeplitz matrices A 0 , A 1 , … , A n with this pattern. As an application we present an elementary proof of a result of D. E. Daykin on the number of n × n Toeplitz matrices over G F ( 2 ) of any specified rank.