منابع مشابه
List-Decoding Multiplicity Codes
We study the list-decodability of multiplicity codes. These codes, which are based on evaluations of high-degree polynomials and their derivatives, have rate approaching 1 while simultaneously allowing for sublinear-time error-correction. In this paper, we show that multiplicity codes also admit powerful list-decoding and local list-decoding algorithms correcting a large fraction of errors. Sta...
متن کاملList decoding of binary codes
We briefly survey some recent progress on list decoding algorithms for binary codes. The results discussed include: – Algorithms to list decode binary Reed-Muller codes of any order up to the minimum distance, generalizing the classical GoldreichLevin algorithm for RM codes of order 1 (Hadamard codes). These algorithms are “local” and run in time polynomial in the message length. – Construction...
متن کاملEfficient List Decoding for Lattices
A sub-optimal decoder for finding K vectors close to a given origin in a lattice is presented. The algorithm operates by partitioning the search space and applying a list version of the sphere decoder, enabling efficient operation for lattices of dimensions m up to and exceeding 200. The decoder is well suited to finding K highly probable sequences for the estimation of a-posteriori probabiliti...
متن کاملList Decoding of Subspace Codes
Codes constructed as subsets of the projective geometry of a vector space over a finite field have recently been shown to have applications as unconditionally secure authentication codes and random network error correcting codes. If the dimension of each codeword is restricted to a fixed integer, the code forms a subset of a finite-field Grassmannian, or equivalently, a subset of the vertices o...
متن کاملCombinatorial bounds for list decoding
Informally, an error-correcting code has “nice” listdecodability properties if every Hamming ball of “large” radius has a “small” number of codewords in it. Here, we report linear codes with non-trivial list-decodability: i.e., codes of large rate that are nicely listdecodable, and codes of large distance that are not nicely list-decodable. Specifically, on the positive side, we show that there...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1992
ISSN: 0012-365X
DOI: 10.1016/0012-365x(92)90528-n