English

Towards the characterization of minimum weight codewords of Schubert codes

Combinatorics 2026-03-17 v1

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\a(,m)C_\a (\ell, m) are given by the so-called \emph{Schubert decomposable codewords}. We prove the validity of the conjecture for all Schubert varieties Ω\a(,Vm)\Omega_{\a}(\ell, V_m) for all but finitely many values of qq.

Keywords

Cite

@article{arxiv.2603.14247,
  title  = {Towards the characterization of minimum weight codewords of Schubert codes},
  author = {Mrinmoy Datta and Tiasa Dutta and Trygve Johnsen},
  journal= {arXiv preprint arXiv:2603.14247},
  year   = {2026}
}