Abstract
We consider the Schubert code \(C_{\alpha }(2, m)\) associated to the \(\mathbb {F}_q\)-rational points of the Schubert variety \(\Omega _{\alpha }(2,m)\) in the Grassmannian \(G_{2,m}\). A correspondence between codewords of \(C_{\alpha }(2, m)\) and skew-symmetric matrices of certain special form is given. Using this correspondence, we give a formula for all possible weights of codewords in \(C_{\alpha }(2, m)\). It is shown that the weight of each codeword is divisible by certain power of q. Further, a formula for the weight spectrum of the Schubert code \(C_{\alpha }(2, m)\) is given.
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Acknowledgements
The authors would like to thank the anonymous referees for their suggestions to improve the article. We would also like to thank S.R. Ghorpade and A.R. Patil for their warm hospitality.
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Communicated by G. McGuire.
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Piñero, F.L., Singh, P. A note on the weight spectrum of the Schubert code \(C_{\alpha }(2, m)\). Des. Codes Cryptogr. 86, 2825–2836 (2018). https://doi.org/10.1007/s10623-018-0477-2
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DOI: https://doi.org/10.1007/s10623-018-0477-2