Gr\"obner Bases for Schubert Codes
Arunkumar R. Patil, Nitin S. Darkunde
TL;DR
This paper explores the computation of Gr"obner bases for binomial ideals linked to linear error-correcting codes, specifically focusing on codes related to Grassmann and Schubert varieties over binary fields, and their application in decoding.
Contribution
It introduces Gr"obner bases for Schubert codes and demonstrates their use in decoding binary Schubert codes, advancing algebraic coding theory methods.
Findings
Derived Gr"obner bases for codes associated with Grassmann and Schubert varieties.
Applied these bases to improve decoding strategies for binary Schubert codes.
Enhanced understanding of algebraic structures underlying error correction.
Abstract
We consider the problem of determining Gr\"obner bases of binomial ideals associated with linear error correcting codes. Computation of Gr\"obner bases of linear codes have become a topic of interest to many researchers in coding theory because of its several applications in decoding and error corrections. In this paper, Gr\"obner bases of linear codes associated to Grassmann varieties and Schubert varieties over a binary field have been obtained. We also use them to study the decoding of binary Schubert codes.
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Taxonomy
TopicsCoding theory and cryptography · Polynomial and algebraic computation · Cryptography and Residue Arithmetic