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- W4315926929 abstract "This paper introduces the partial-inverse problem for linearized polynomials and develops its application to decoding Gabidulin codes and lifted Gabidulin codes in linear random network coding. The proposed approach is a natural generalization of its counterpart for ordinary polynomials, thus providing a unified perspective on Reed–Solomon codes for the Hamming metric and for the rank metric. The basic algorithm for solving the partial-inverse problem is a common parent algorithm of a Berlekamp–Massey algorithm, a Euclidean algorithm, and yet another algorithm, all of which are obtained as easy variations of the basic algorithm. Decoding Gabidulin codes can be reduced to the partial-inverse problem via a key equation with a new converse. This paper also develops new algorithms for interpolating crisscross erasures and for joint decoding of errors, erasures, and deviations in random network coding." @default.
- W4315926929 created "2023-01-14" @default.
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- W4315926929 creator A5081994957 @default.
- W4315926929 date "2023-06-01" @default.
- W4315926929 modified "2023-10-16" @default.
- W4315926929 title "The Partial-Inverse Approach to Linearized Polynomials and Gabidulin Codes With Applications to Network Coding" @default.
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- W4315926929 doi "https://doi.org/10.1109/tit.2023.3236720" @default.
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