04158556

j

04158556 Ryan, Charles T. Ryan, Kevin M. The minimum weight of the Grassmann codes C(k,n). Discrete Appl. Math. 28, No.2, 149-156 (1990). 1990 Elsevier Science B.V. (North-Holland), Amsterdam EN linear block codes Grassmann variety Pl\"ucker coordinates minimum weight affine charts

doi:10.1016/0166-218X(90)90112-P

Summary: In this paper we continue the investigation of a family of linear block codes based on the geometry of the Grassmann variety G(k,n) of k-planes in the n-dimensional vector space over ${\bbfZ}\sb 2$. These codes, denoted by C(k,n), have as their generator matrix the $(\frac{n}{k})\times \vert G(k,n)\vert$ matrix whose columns are the Pl\"ucker coordinates of the points of G(k,n). The major results established herein are: The minimum weight of C(k,n) is equal to $2\sp{k(n-k)}$. The number of codewords in C(k,n) of minimal weight is equal to $\vert G(k,n)\vert$. The minimal weight codewords of C(k,n) are the affine charts of G(k,n).