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

Authors:
Irene Márquez-Corbella;Edgar Martínez-Moro;Ruud Pellikaan
Affiliations:
Institute of Mathematics and Department of Algebra, Geometry and Topology, University of Valladolid, Valladolid, Spain 47005;Institute of Mathematics and Department of Applied Mathematics, University of Valladolid, Castilla, Spain;Department of Mathematics and Computing Science, Eindhoven University of Technology, Eindhoven, The Netherlands 5600 MB
Venue:
Designs, Codes and Cryptography
Year:
2013

Citing 7
Cited 2

How to Mask the Structure of Codes for a Cryptographic Use

Designs, Codes and Cryptography
Cryptanalysis of the niederreiter public key scheme based on GRS subcodes

PQCrypto'10 Proceedings of the Third international conference on Post-Quantum Cryptography
Grover vs. mceliece

PQCrypto'10 Proceedings of the Third international conference on Post-Quantum Cryptography
An attack on a modified niederreiter encryption scheme

PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
New generalizations of the Reed-Muller codes--I: Primitive codes

IEEE Transactions on Information Theory
New directions in cryptography

IEEE Transactions on Information Theory
On the equivalence of McEliece's and Niederreiter's public-key cryptosystems

IEEE Transactions on Information Theory

On the unique representation of very strong algebraic geometry codes

Designs, Codes and Cryptography
Computational aspects of retrieving a representation of an algebraic geometry code

Journal of Symbolic Computation

Quantified Score

Hi-index	0.00

Visualization

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.