The non-gap sequence of a subcode of a generalized Reed-Solomon code
Abstract
This paper addresses the question of how often the square code of an arbitrary l-dimensional subcode of the code GRSk(a; b) is exactly the code GRS2k-1(a; b * b). To answer this question we rst introduce the notion of gaps of a code which allows us to characterize such subcodes easily. This property was rst stated and used in [10] where Wieschebrink applied the Sidelnikov-Shestakov attack [8] to brake the Berger-Loidreau cryptostystem [1].
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