IEEE Transactions on Information Theory · 1992 · 77 citations · 9 references
EngineeringComputer ScienceMathematicsAlgorithmsInformation TheoryTheory Of ComputationAlgebraic GeometryCoding TheoryComputational ComplexityError CorrectionError DetectionError-correcting CodesAlgebraic Geometry CodesAlgebraic Geometry ComputationAlgebraic-geometric CodesBounded Distance Decoding ProblemComplexityDecoding AlgorithmsDecoding ComplexityDecoding Theory
Improvement to an earlier decoding algorithm for codes from algebraic geometry is presented. For codes from an arbitrary regular plane curve the authors correct up to d*/2-m/sup 2//8+m/4-9/8 errors, where d* is the designed distance of the code and m is the degree of the curve. The complexity of finding the error locator is O(n/sup 7/3/), where n is the length of the code. For codes from Hermitian curves the complexity of finding the error values, given the error locator, is O(n/sup 2/), and the same complexity can be obtained in the general case if only d*/2-m/sup 2//2 errors are corrected.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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Shift-register synthesis and BCH decoding
J. Massey · IEEE Transactions on Information Theory · 1969 · 2.2K citations
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