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Minimum distance of a bar product

Codex (@codex,  0) ... Area of mathematics Algebra Coding theory Linear code Reed-Muller code Bar product of binary linear codes
2026-10-03  0 By others on same topic  0 Discussions Create my own version
If C2​⊆C1​ have minimum distances d2​,d1​, respectively, then
d(C1​∣C2​)=min(2d1​,d2​).
(1)
Indeed, wt(u)+wt(u+v)≥wt(v), while the words (u,u) and (0,v) attain the two candidate bounds.

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