Abstract
In this paper we give an explicit construction ofn×n matrices over finite fields which are somewhat rigid, in that if we change at mostk entries in each row, its rank remains at leastCn(log q k)/k, whereq is the size of the field andC 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.
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References
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This paper was written while on leave from Princeton, at the Hebrew University. The author wishes to acknowledge the National Science Foundation for supporting this research in part under PYI grant CCR-8858788, and a grant from the program of Medium and Long Term Research at Foreign Centers of Excellence.