Standard Bases for Linear Codes over Prime Fields
Jean Jacques Ferdinand Randriamiarampanahy, Harinaivo Andriatahiny,, Toussaint Joseph Rabeherimanana
TL;DR
This paper introduces a method for representing linear codes over prime fields using standard bases of binomial ideals within localized polynomial rings, enhancing algebraic analysis of such codes.
Contribution
It provides the first construction of standard bases for ideals associated with linear codes over prime fields in localized polynomial rings.
Findings
Standard bases facilitate algebraic analysis of linear codes.
The method applies to codes over prime fields.
Enhances understanding of code structure through algebraic tools.
Abstract
It is known that a linear code can be represented by a binomial ideal. In this paper, we give standard bases for the ideals in a localization of the multivariate polynomial ring in the case of linear codes over prime fields.
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