Gr\"obner Bases for Schubert Codes

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.