On t-revealing codes in binary Hamming spaces

Abstract

In this paper, we introduce t-revealing codes in the binary Hamming space Fn. Let C⊆Fn be a code and denote by It(C;x) the set of elements of C which are within (Hamming) distance t from a word x∈Fn. A code C is t-revealing if the majority voting on the coordinates of the words in It(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.