List decoding of Reed-Solomon codes from a Gröbner basis perspective
نویسندگان
چکیده
The interpolation step of Guruswami and Sudan’s list decoding of Reed-Solomon codes poses the problem of finding the minimal polynomial of an ideal with respect to a certain monomial order. An efficient algorithm that solves the problem is presented based on the theory of Gröbner bases of modules. In a special case, this algorithm reduces to a simple Berlekamp-Massey-like decoding algorithm.
منابع مشابه
Sudan’s List Decoding of Reed-Solomon Codes from a Gröbner Basis Perspective
The interpolation step of Sudan’s list decoding of Reed-Solomon codes sets forth the problem of finding the minimal polynomial of an ideal with respect to a certain monomial order. An efficient algorithm that solves the problem is presented based on the theory of Gröbner bases of modules. In a special case, this algorithm is shown to be equivalent with the Berlekamp-Massey algorithm for decodin...
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ورودعنوان ژورنال:
- J. Symb. Comput.
دوره 43 شماره
صفحات -
تاریخ انتشار 2008