Unique Decoding of Certain Reed-Solomon Codes

Lin-Zhi SHEN  Fang-Wei FU  Xuan GUANG  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E98-A   No.12   pp.2728-2732
Publication Date: 2015/12/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E98.A.2728
Type of Manuscript: LETTER
Category: Coding Theory
Reed-Solomon code,  interleaved Reed-Solomon code,  multi-sequence shift-register synthesis,  virtual extension,  decoding radius,  

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In this paper, we consider the Reed-Solomon codes over Fqm with evaluations in a subfield Fq. By the “virtual extension”, we can embed these codes into homogeneous interleaved Reed-Solomon codes. Based on this property and the collaborative decoding algorithm, a new probabilistic decoding algorithm that can correct errors up to $ rac{m}{m+1}(n-k)$ for these codes is proposed. We show that whether the new decoding algorithm fails or not is only dependent on the error. We also give an upper bound on the failure probability of the new decoding algorithm for the case s=2. The new decoding algorithm has some advantages over some known decoding algorithms.