A note on the weight spectrum of the Schubert code $$C_{\alpha }(2, m)$$ C α ( 2 , m )

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.