4 Limits to List Decodability

Abstract

The previous chapter showed that every code of certain minimum distance has an associated “Johnson radius” which gives a lower bound on the list decoding radius (in other words, every Hamming ball of radius up to the Johnson radius has “few” codewords). This result plays an important role in the development of the subject of list decoding. Indeed, by showing that any code with large distance has large list decoding radius, it raises algorithmic questions concerning list decoding important families of codes beyond half the minimum distance.