Re: S-box related design question

David Rush <[EMAIL PROTECTED]> writes:

>I want to map m-bit integers to n-bit integers (m < n) in such a way that
>the bitwise difference between all the m^2 pairs of n-bit integers (as
>measured by counting the 1 bits remaining after xor) is maximised. It
>strikes me that this problem is very similiar to S-box construction or
>(even more likely) error-correction code construction. The big difference
>is that n > 2*m in all of the cases I am needing to handle. Most error-code
>construction is dealing with cases where 2*m > n > m+2.

>Can anyone suggest ideas or point me to on-line resources for more
>information?

This is exactly the problem of constructing an error correcting code with
the maximum Hamming distance.  You might start with Appendix A in the back
of "The theory of error correcting codes" by MacWilliams and Sloane.  This
appendix gives the best known codes, as a function of word size, up to 
Hamming weight of 29.  Many of these are in your range of interest.  
For example, if you want to map 8 bit values into words that differ by at 
least 17 bits, you will need 43 bit words, using construction 
'GP' (Goppa codes) from reference 1217.

      Lou Scheffer