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...
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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 linearcodes. First, based on the idea of constructing polynomialscodes over F-q, we construct a class of polynomial functions by using the circular permutation defined over F-q, and a new type of linearcodes 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 linearcodes. It turns out that some codes from this construction have good parameters based on Brouwer's table.
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...
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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 issignificantly reduced from 256 to 4. At the same time, the circuit issimplified 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 codesignal 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.
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