A word of weight w and length n is called regular if in every interval [(i-1)(n/w), i(n/w)) it contains exactly one nonzero entry for all 0 < i < w+1 .
There are exactly (n/w)^w different regular words of weight w and length n, so we need exactly \log((n/w)^w)= w \log(n/w) = s bits of data to encode these regular words.