## 摘要

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.

原文 | English |
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頁（從 - 到） | 1 |

頁數 | 1 |

期刊 | IEEE Transactions on Information Theory |

DOIs | |

出版狀態 | Accepted/In press - 2023 |