Coding theory MOC

Binary linear code

The vector space is equivalent to the powerset where is a set with elements, and addition is given by symmetric difference. code Thus a binary linear code is a -subspace of .¹ Indeed, the main advantage of this notation is that it allows the importing of notations from set theory.

• FLM code types I and II

• Orthogonal code

Further notions

• Given a codeword we have .
• The natural non-singular symmetric bilinear form on becomes .
• Even binary code
• Lattice from a binary linear code

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Footnotes

1. 1988. Vertex operator algebras and the Monster, §10.1, p. 299 ↩