Distance-increasing mappings from binary vectors to constant composition vectors

Abstract

A distance-preserving mapping is a one-to-one function f from p-ary vectors of length m to q-ary vectors of length n such that any two distinct p-ary vectors are mapped to two different q-ary vectors with an equal or greater Hamming distance. A special distance-preserving mapping called a distance-increasing mapping is a mapping which increases the distance at least one if the distance of two distinct input strings are not equal to the output length. A constant composition vector is a vector under the restriction that each alphabet symbol occurs a given number of times. In this paper, we propose a distance-increasing mapping from binary vectors to constant composition quaternary vectors. We also give an optimal impossibility result for constructing distance-preserving mapping from binary vectors to constant composition ternary vectors in the so-called swapping model.