IEEE Transactions on Information Theory · 1993 · 67 citations · 6 references
ComputingComputer EngineeringComputer ScienceAlgorithmsComputational GeometryCryptographyCoding TheoryError Control CodingError-correcting CodesAlgebraic Geometry CodesAlgebraic-geometric CodesDecoding AlgorithmsMinimum DistanceSyndrome Decoding Problem
A majority coset decoding (MCD) procedure that can be applied to an arbitrary geometric code is discussed. In general, the basic algorithm for decoding of algebraic-geometric codes does not correct up to the designed minimum distance. In MCD, a reduction step is added to the basic algorithm. In case the basic algorithm fails, a majority scheme is used to obtain an additional syndrome for the error vector. Thus a strictly smaller cost containing the error vector is obtained. In this way, the basic algorithm is applied to a decreasing chain of cosets and after finitely many steps the coset will be small enough for successful application of the basic algorithm.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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Construction and decoding of a class of algebraic geometry codes
J. Justesen, Knud J. Larsen, H.E. Jensen et al. · IEEE Transactions on Information Theory · 1989 · 127 citations · Full text