Entropic Generation of Binary Words

The uniform generation of k Hamming weight binary words, equivalent to sampling k-subsets from n elements, relies on random bits, which can be expensive.We introduce a novel paradigm-random bit recycling-and use it to generate such binary words in linear time while consuming as few random bits as possible.The resulting algorithm is nearly optimal in terms of random bit consumption, meaning that it closely matches the Shannon entropic lower bound coming from information theory.