The Weight Distribution of a Family of Lagrangian-Grassmannian Codes

摘要

Using Pliicker coordinates we construct a matrix whose columns parametrize all projective isotropic lines in a symplectic space E of dimension 4 over a finite field F_q. As an application of this construction we explicitly obtain the smallest subfamily of algebro-geometric codes defined by the corresponding Lagrangian-Grassmannian variety. Furthermore, we show that this subfamily is a class of three-weight linear codes over (IF), of length (q~4 - 1)/(q - 1), dimension 5, and minimum Hamming distance q~3 - q.