List decoding algorithms for certain concatenated codes

Abstract

We give efficient (polynomial-time) list-decoding algorithms for certain families of error-correcting codes obtained by "concatenation". Specifically, we give list-decoding algorithms for codes where the "outer code" is a Reed-Solomon or Algebraic-geometric code and the "inner code" is a Hadamard code. Codes obtained by such concatenation are the best known constructions of errorcorrecting codes with very large minimum distance. Our decoding algorithms enhance their nice combinatorial properties with algorithmic ones, by decoding these codes up to the currently known bound on their list-decoding "capacity". In particular, the number of errors that we can correct matches (exactly) the number of errors for which it is known that the list size is bounded by a polynomial in the length of the codewords. © 2000 ACM.