Handbook of Coding Theory
Multivariate polynomials in coding theory
AAECC-2 Proceedings of the 2nd International Conference on Applied Algebra, Algorithms and Error-Correcting Codes
Partial permutation decoding for codes from finite planes
European Journal of Combinatorics
Information-set decoding for linear codes over Fq
PQCrypto'10 Proceedings of the Third international conference on Post-Quantum Cryptography
The complexity of information set decoding
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Permutation decoding of abelian codes
IEEE Transactions on Information Theory
Information sets and partial permutation decoding for codes from finite geometries
Finite Fields and Their Applications
Information Sets From Defining Sets in Abelian Codes
IEEE Transactions on Information Theory
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In Bernal and Simón (IEEE Trans Inf Theory 57(12):7990---7999, 2011) we introduced a technique to construct information sets for every semisimple abelian code by means of its defining set. This construction is a non trivial generalization of that given by Imai (Inf Control 34:1---21, 1977) in the case of binary two-dimensional cyclic (TDC) codes. On the other hand, Sakata (IEEE Trans Inf Theory IT-27(5):556---565, 1981) showed a method for constructing information sets for binary TDC codes based on the computation of Groebner basis which agrees with the information set obtained by Imai. Later, Chabanne (IEEE Trans Inf Theory 38(6):1826---1829, 1992) presents a generalization of the permutation decoding algorithm for binary abelian codes by using Groebner basis, and as a part of his method he constructs an information set following the same ideas introduced by Sakata. In this paper we show that, in the general case of q-ary multidimensional abelian codes, both methods, that based on Groebner basis and that defined in terms of the defining sets, also yield the same information set.