Improved codes for list decoding in the Levenshtein's channel and information retrieval

In this paper, we introduce t-revealing codes in the binary Hamming space F
ⁿ
. Let C ⊆ F
ⁿ
be a code and denote by I
_t
{C; x) the set of codewords of C which are within (Hamming) distance t from a word x ϵ F
ⁿ
. A code C is t-revealing if the majority voting on the coordinates of the words in I
_t
(C; x) gives unambiguously x. These codes have applications, for instance, to the list decoding problem of the Levenshtein's channel model, where the decoder provides a list based on several different outputs of the channel with the same input, and to the information retrieval problem of the Yaakobi-Bruck model of associative memories. We give t-revealing codes which improve some of the key parameters for these applications compared to earlier code constructions, namely, the length of the output list L of the decoder and the maximal number of input clues m needed for information retrieval.