Let $A$ and $B$ be two binary $(n,M,d)$ codes. We define $a_i = \#\{(w_1,w_2) \in A^2:\:d(w_1,w_2) = i\}$, and same for $b_i$. If $a_i = b_i$ for all $i$, can one deduct that $A$ and $B$ are equivalent, i.e. equal up to permutation of positions and permutation of letters in a fixed position?
Do equal distance distributions imply equivalence?
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information-theory
coding-theory
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2Isn't this the same as http://mathoverflow.net/questions/102339/a-different-criterion-for-equivalence-of-codes, which has been answered? – 2012-07-17
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0@Gerry: looks like it is, but I don't seem to find a real example in any of the papers? – 2012-07-17