Coding theory MOC

Binary linear code

The vector space 𝕂𝑛2 is equivalent to the powerset P(Ω𝑛) where Ω𝑛 is a set with 𝑛 elements, and addition is given by symmetric difference. code Thus a binary linear code C is a GF⁡(2)-subspace of P(Ω𝑛).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 𝐶 ∈C we have wt⁡𝐶 =|𝐶|.
• The natural non-singular symmetric bilinear form on P(Ω𝑛) becomes |𝑆1∩𝑆2| +2ℤ.
• Even binary code
• Lattice from a binary linear code

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develop | en | SemBr

Footnotes

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