Application of a fast simulation method to the estimation of the number of some k-dimensional subspaces over a finite space

Abstract

A fast simulation method is proposed for estimation of the number of k-dimensional subspaces of weight w in an n-dimensional vector space over the Galois field containing q components. Unbiased estimates are constructed for the cases when w?=?1 and w?=?2, and lower and upper estimates are proposed for the case when w?=?3. It is proved that the relative error remains bounded as q????. A high accuracy of the method proposed is illustrated by numerical examples.