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a perfect code is a code where an equal number of received values decode to the same message for all messages (loose translation).
a cyclic code is a code where all cyclic shifts of a codeword are also codewords.
A perfect cyclic code would have both properties. for example, the binary golay code, G23, can be formulated as a perfect cyclic code.
luben may be thinking of LFSR's and maximal length sequences (2^N -1), though somewhat mixes this with a de Bruijen sequence (2^N).
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