A NOTE ON MATRIX RIGIDITY

In this paper we give an explicit construction of n x n matrices over finite fields which are somewhat rigid, in that if we change at most k entries in each row, its rank remains at least Cn(log(q) k)/k, where q is the size of the field and C is an absolute constant. Our matrices satisfy a somewhat stronger property, we will explain and call ''strong rigidity''. We introduce and briefly discuss strong rigidity, because it is in a sense a simpler property and may be easier to use in giving explicit construction.