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Journals and Conferences
In this paper we introduce a binomial ideal derived from a binary linear code. We present some applications of a Gröbner basis of this ideal with respect to a total degree ordering. In the first application we give a decoding method for the code. In the second one, by associating the code with the set of cycles in a graph, we can solve the problem of… (More)
This article aims to explore the bridge between the algebraic structure of a linear code and the complete decoding process. To this end, we associate a specific binomial ideal I+(C) to an arbitrary linear code. The binomials involved in the reduced Gröbner basis of such an ideal relative to a degreecompatible ordering induce a uniquely defined test-set for… (More)
Niederreiter and Xing (2000) recently proposed a propagation rule for linear codes.O/spl uml/zbudak and Stichtenoth showed that the Niederreiter-Xing construction is a particular construction of a matrix-product code. Cheng, Cheng, and Sun analyzed the case when Niederreiter-Xing rule commutes with duality. The aim of this correspondence is to generalize… (More)
This paper addresses the question of how often the square code of an arbitrary l-dimensional subcode of the code GRSk(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 stated and used in  where Wieschebrink… (More)
It has been widely known that complete decoding for binary linear codes can be regarded as an linear integer programming problem with binary arithmetic conditions. Conti and Traverso  have proposed an efficient algorithm which uses Gröbner bases to solve integer programming with ordinary integer arithmetic conditions. Ikegami and Kaji  extended the… (More)
In this paper we introduce the class of composite access structures for secret sharing. We also provide secret sharing schemes realizing these structures and study their information rates. As a particular case of this construction, we present the subclass of iterated threshold schemes, a large class of ideal secret sharing schemes.
This paper addresses the question of retrieving the triple (X ,P, E) from the algebraic geometry code C = CL(X ,P, E), where X is an algebraic curve over the finite field Fq, P is an n-tuple of Fq-rational points on X and E is a divisor on X . If deg(E) ≥ 2g + 1 where g is the genus of X , then there is an embedding of X onto Y in the projective space of… (More)
In this work we consider repeated-root multivariable codes over a finite chain ring. We show conditions for these codes to be principally generated. We consider a suitable set of generators of the code and compute its minimum distance. As an application we study the relevant example of the generalized Kerdock code in its r -dimensional cyclic version.