Efficient encoding via Gröbner bases and discrete Fourier transforms for several kinds of algebraic codes
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چکیده
Abstract—Novel encoding scheme for algebraic codes, such as codes on algebraic curves, multidimensional cyclic codes, and hyperbolic cascaded Reed–Solomon codes, is proposed with numerical examples. We make use of the 2-dimensional inverse discrete Fourier transform, which generalizes the Mattson–Solomon polynomial for Reed–Solomon codes. We also generalize the workings of the generator polynomial for Reed–Solomon codes, and realize a systematic encoding for various algebraic codes.
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تاریخ انتشار 2008