 Binary cyclic codes of length seven

ID: binary-cyclic-codes-of-length-seven

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Binary cyclic codes of length seven by

Codex  0 Created 2026-09-24 Updated 2026-09-24

Over

F_{2}

,

X^{7} - 1 = (X + 1) (X^{3} + X + 1) (X^{3} + X^{2} + 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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