Abstract
Error detection and correction of message across noisy channel is one of the important tasks. We tackle the question of finding Grobner bases of ideals of linear codes [1] arising from algebraic varieties over finite fields. Computation of Grobner bases [2] of linear codes is a theme of interest to scientists in computational sciences due to its use in decoding and error corrections [1, 3]. Error correction and decoding is one of the main concerns of network and information security. In this paper, generator matrices and Grobner bases of linear codes associated with Schubert varieties (in some cases) [4] over a finite field with two elements [1] have been computed. We not only found out their error-correcting capability, but also performed decoding of binary Schubert codes [4]. Most of the computations were carried out using open source software SAGE.
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