Abstract
This paper addresses the question how often the square code of an arbitrary l-dimensional subcode of the code GRS k (a, b) is exactly the code GRS2k-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 used and stated by Wieschebrink where he applied the Sidelnikov–Shestakov attack to break the Berger–Loidreau cryptosystem.
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This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Coding and Cryptography”.
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Márquez-Corbella, I., Martínez-Moro, E. & Pellikaan, R. The non-gap sequence of a subcode of a generalized Reed–Solomon code. Des. Codes Cryptogr. 66, 317–333 (2013). https://doi.org/10.1007/s10623-012-9694-2
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DOI: https://doi.org/10.1007/s10623-012-9694-2