Towards the characterization of minimum weight codewords of Schubert codes
Abstract
A conjectural formula for the minimum weight of Schubert codes was conjectured by Ghorpade in 2000. This was established by Xiang in 2008. In 2018, Ghorpade and Singh provided a new proof of this conjecture. Moreover, they also conjectured that the minimum weight codewords of the Schubert codes C (, m) are given by the so-called Schubert decomposable codewords. We prove the validity of the conjecture for all Schubert varieties (, Vm) for all but finitely many values of q.
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