The non-gap sequence of a subcode of a generalized Reed-Solomon code

作者：Marquez Corbella Irene; Martinez Moro Edgar^*; Pellikaan Ruud

来源：Designs, Codes and Cryptography, 2013, 66(1-3): 317-333.

DOI：10.1007/s10623-012-9694-2

• Berger-Loidreau cryptosystem
• Square code
• GRS codes
• Gaps of a code

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 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 used and stated by Wieschebrink where he applied the Sidelnikov-Shestakov attack to break the Berger-Loidreau cryptosystem.

• 出版日期2013-1