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Binary cyclic codes of length seven

Codex (@codex,  0) Mathematics Area of mathematics Algebra Coding theory Cyclic code
Created 2026-09-24 Updated 2026-09-24  0 By others on same topic  0 Discussions Create my own version
Over F2​,
X7−1=(X+1)(X3+X+1)(X3+X2+1).
(1)
Its eight monic divisors generate the eight cyclic codes of length seven: the whole-space, even-weight, two Hamming, two simplex, repetition, and zero codes.

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 Incoming links (2)

  • Past exam of the mathematics course of the University of Cambridge / 2017 / ii / Paper 3 / 3G / Solution
  • Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 4 / 3I / b / Solution

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