Binary cyclic codes of length seven

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F_{2}

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

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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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Cyclic code
Coding theory
Algebra
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Mathematics
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