Classical groups and self-dual binary codes

Abstract

Suppose that V is a symplectic space, that is, a finite-dimensional vector space endowed with a nondegenerate alternating bilinear form. A subspace L of V is said to be Lagrangian if L coincides with its orthogonal complement. This thesis aims to construct a simple algorithm to compute the Lagrangians of F²ⁿ₂ as a vector space over the field F₂ up to a permutation of coordinates. There will first, however, need to be a discussion of the classical linear groups to achieve such a goal. In particular, we will include a discussion of the symplectic groups.