Details:
Title  Information sets in abelian codes: defining sets and Groebner basis.  Author(s)  Jose Joaquin Bernal, Juan Jacobo Simon  Type  Article in Journal  Abstract  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 twodimensional cyclic (TDC) codes. On the other hand, Sakata (IEEE Trans Inf Theory IT27(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 qary 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.  Keywords  Abelian codes, Information sets, Permutation decoding  ISSN  09251022; 15737586/e 
URL 
http://link.springer.com/article/10.1007%2Fs106230129735x 
Language  English  Journal  Des. Codes Cryptography  Volume  70  Number  12  Pages  175188  Publisher  Springer US, New York, NY  Year  2014  Edition  0  Translation 
No  Refereed 
No 
