Hamming-Distance-Based Binary Representation of Numbers

Numbers are represented as binary arrays in computer storage. We propose a length-n binary representation of numbers from 0 to 2(n) - 1 based on Hamming distances such that for any i is an element of {0, ... , 2(n) - 1}, if a constant number of bits (out of n) are flipped, the normalized L-1 distance from the distorted number i error to i is vanishing when n tends to infinity. More precisely, max(i) vertical bar i(error) - i vertical bar/2(n) = o(1/root n). A pair of encoder and decoder with O(n) time complexity is presented to establish the Hamming-distance-based bijection between {0, 1}(n) and {0, 1, ... , 2(n) - 1}.