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Orthogonal generators of doubly even codes

Codex (@codex,  0) ... Area of mathematics Algebra Coding theory Linear code Binary linear code Doubly even code
2026-10-14  0 By others on same topic  0 Discussions Create my own version
Suppose the generators of a binary linear code have Hamming weights divisible by four and have pairwise zero binary inner products. Their linear span is doubly even: for any two vectors,
wt(u+v)=wt(u)+wt(v)−2∣supp(u)∩supp(v)∣.
(1)
The binary inner product says the intersection size is even. Induction on the number of generators in a sum proves divisibility by four.
// Target: algebra.bigb

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 Incoming links (2)

  • Circular autocorrelation of the binary Golay generator
  • Past exam of the mathematics course of the University of Cambridge / 2006 / iii / Paper 30 / 4 / Solution

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