Classical groups and self-dual binary codes

King, Patrick H. (2024) Classical groups and self-dual binary codes. Memorial University of Newfoundland. (Unpublished)

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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.

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