Introduction to Reed - Solomon Codes
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A general construction of Reed-Solomon codes based on generalized discrete Fourier transform
In this paper, we employ the concept of the Generalized Discrete Fourier Transform, which in turn relies on the Hasse derivative of polynomials, to give a general construction of Reed-Solomon codes over Galois fields of characteristic not necessarily co-prime with the length of the code. The constructed linear codes enjoy nice algebraic properties just as the classic one.
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Journal of the Society for Industrial and Applied Mathematics. In June of 1960 the paper was published: five pages under the rather unpretentious title "Polynomial Codes over Certain Finite Fields" [17]. This paper described a new class of error-correcting codes that are now called Reed-Solomon codes. In the decades since their discovery, Reed-Solomon codes have enjoyed countless applications, ...
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4 Ideals and cyclic codes 18 4.1 Ideals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.2 Cyclic codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 4.3 Group of a code . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4.4 Minimal polynomials . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.5 BCH and Reed-Solomon codes . . . . . . . . . . ....
متن کاملReed - Solomon Hybrid Codes For Optical Communications
The astonishing performance of concatenated codes attracted many researchers and this has resulted in an explosive amount of literature since their introduction few years ago. As concatenation between codes did not actually arise from applying a pre-existing theory, most of their outstanding features remain to be explained. This paper gives some explanation of the concatenation between Reed Sol...
متن کاملAn Efficient SISO Algorithm for Reed-Solomon Codes
There has been renewed interest in iterative decoding algorithms for concatenated codes since the introduction of Turbo codes. Such iterative methods are built on top of soft-insoft-out algorithms. Powerful concatenated codes may be constructed with linear block codes codes as constituent codes. Such codes can be better alternatives to Turbo Codes either when high coding rates or when short int...
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تاریخ انتشار 2011