Abstract. This paper addresses the question of how often the square code of an arbitrary l-dimensional subcode of the code GRS k (a, b) is exactly the code GRS 2k−1 (a, b * b). To answer this question we first introduce the notion of gaps of a code which allows us to characterize such subcodes easily. This property was first stated and used in [10] where Wieschebrink applied the Sidelnikov-Shestakov attack [8] to brake the Berger-Loidreau cryptostystem [1].