Efficient generation of binary words of given weight

Abstract

We thus provide here a linear time encoder/decoder of binary sequences into words of given weight and length. Furthermore, our algorithm is easy to implement and requires a limited amount of memory. Any exact solution, that a bijection between W _n,t and {1,2,..., (n/t)} will require, as far as we know, an algorithm of complexity at least O(n ²), and computations over large integers.

It must be noted however that the statistical properties of the words generated are not very good. The major drawback being that the average length of the last sequence of consecutive “0”s is much larger than the other. For instance with n=1024, t=50 and K=80 the length of this last sequence is 124 instead of 20.