Binary linear code

FLM code types I and II

In Vertex operator algebras and the Monster, a binary linear code is said to be type I iff

1. ;
2. for all , i.e. is an even code; and

and type II iff

1. ;
2. for all , i.e. is an doubly even code; and

It follows that such codes are subcodes of the even binary code.

Properties

1. Let . Then is self-orthogonal code of type II iff is a (maximal) totally isotropic subspace of of dimension ; equivalently is a (maximal) totally isotropic subspace of of dimension .

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