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I am a newbie in error correcting codes and interested to understand binary BCH codes. I understand that all the code words are at least in dmin = 2t+1 Hamming distance of each other. But I have the following questions.

  1. Is there any relationship between the Hamming distance between input and output of a BCH encoder? e.g. Dose closer inputs have closer code words (outputs) after encoding?

  2. Is there a tight upper bound on the Hamming distance of the code words (i.e. dmax)?

  3. What is the number of unique code words than can be generated? Is it exactly 2^k or actually less than this?

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