On the linear codes arising from Schubert varieties (Q702177)

Codes from Schubert varieties were introduced by \textit{S. R. Ghorpade} and \textit{G. Lachaud} [in Coding theory, cryptography and related areas (Guanajuato, 1998), 122--131, Springer, Berlin (2000; Zbl 1021.94026)] as the codes corresponding to the projective system defined by Schubert subvarieties of Grassmann varieties \(\text{ Gr}(l,m)\). In this paper, the autors give a lower bound on the minimum distance of these codes. Furthermore, for the particular case of the code coming from a Schubert variety of lines, the full distribution of weights (and hence the true minimum distance) is computed.