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Constructions of Polynomial codes Based on Circular Permutation Over Finite Fields

IEEE ACCEss 2020年 8卷 134219-134223页

作者： Wang, Xiuli Hao, Yakun Qiao, Dan Civil Avit Univ China Coll Sci Tianjin 300300 Peoples R China

As a kind of very important error-correcting codes, polynomial codes have the advantages of good performance and simple structure. Generalized r-s codes over F-q as polynomial codes have the advantages described above, but their lengths n are at most q. In order to increase the length of the codes, in this paper, we apply a method similar to the construction of the generalized r-s codes over F-q and develop Ling and Xing's idea to construct new q-ary linear codes. First, based on the idea of constructing polynomials codes over F-q, we construct a class of polynomial functions by using the circular permutation defined over F-q, and a new type of linear codes is constructed from the properties of these functions and Mobius functions. Then, we give the value of the length n, the dimension k and the lower bound of the minimum distance d of the new linear codes. It turns out that some codes from this construction have good parameters based on Brouwer's table.

关键词： Polynomial code r-s code circular permutation Mobius function

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FAsT ALGOrITHM FOr rEED-sOLOMON code AND THE HArDWArE IMPLEMENTATION

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Transactions of Tianjin University 1995年第1期1卷 83+80-83页

作者：张毓忠滕建辅周长华

This paper described a signal processor for the reed-solomon (r-s) code using micro-programming. For the purpose of fast encoding and decoding,a formula for detecting two errors is derived, and the Qian search method for the decoding process is improved. The number of searches is significantly reduced from 256 to 4. At the same time, the circuit is simplified and the speed is increased. For the convenience of programming, a micro-programming compiling package is developed. The package can be used for programming of different formats of r-s code signal processors of DAB, MD and DCC. The software and the hardware can be used for error correcting, error detecting and error compensation of different formats of r-s code.

关键词： r-s code encoding decoding Qian search

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