On the ideal associated to a linear code
نویسندگان
چکیده
منابع مشابه
On the ideal associated to a linear code
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 the code, and this allows the descript...
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چکیده ندارد.
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We will show how one can compute all reduced Gröbner bases with respect to a degree compatible ordering for code ideals even though these binomial ideals are not toric. To this end, the correspondence of linear codes and binomial ideals will be briefly described as well as their resemblance to toric ideals. Finally, we will hint at applications of the degree compatible Gröbner fan to the code e...
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In this work we study a weak order ideal associated with the coset leaders of a non-binary linear code. This set allows the incrementally computation of the coset leaders and the definitions of the set of leader codewords. This set of codewords has some nice properties related to the monotonicity of the weight compatible order on the generalized support of a vector in F q which allows to descri...
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The rings considered in this article are commutative with identity which admit at least two maximal ideals. This article is inspired by the work done on the comaximal ideal graph of a commutative ring. Let R be a ring. We associate an undirected graph to R denoted by mathcal{G}(R), whose vertex set is the set of all proper ideals I of R such that Inotsubseteq J(R), where J(R) is...
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ژورنال
عنوان ژورنال: Advances in Mathematics of Communications
سال: 2016
ISSN: 1930-5346
DOI: 10.3934/amc.2016003