Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let $H_r$ be the usual Hamming code of length $2^r-1$. What is the weight enumerator of $H_r^\perp$? Using this find an expression for the weight enumerator of $H_r$. (we are in binary case)

share|improve this question

1 Answer 1

Hints:

  1. The duals of the Hamming codes are the Simplex codes. The Simplex codes are "constant weight codes", since all nonzero codewords have the same weight. Can you find the weight enumerator of the Simplex codes from this information?

  2. The weight enumerators of the primal and the dual code are related by the MacWilliams identities. Use this to translate the weight enumerator of the Simplex codes into the weight enumerator of the Hamming codes.

share|improve this answer
    
thank you azimut i will try to use your hints –  juliet May 10 '13 at 21:16

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.