On Multisequence Shift Register Synthesis and Generalized-Minimum-Distance Decoding of Reed-Solomon Codes
نویسندگان
چکیده
منابع مشابه
Unambiguous Decoding of Generalized Reed–Solomon Codes Beyond Half the Minimum Distance
The Schmidt–Sidorenko–Bossert scheme extends a low-rate Reed–Solomon code to an Interleaved Reed–Solomon code and achieves the decoding radius of Sudan’s original list decoding algorithm while the decoding result remains unambiguous. We adapt this result to the case of Generalized Reed– Solomon codes and calculate the parameters of the corresponding Interleaved Generalized Reed–Solomon code. Fu...
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We present an efficient erasure decoding algorithm for generalized Reed Solomon codes constructed by utilizing the structure of the inverse of the VanderMonde matrices. Given an [n, k] generalized Reed Solomon code, decoding for r erasures, where r = n − k, requires rk + n Galois field multiplications and r(k − 1) Galois field additions after setting up the decoding structures for an erasure pa...
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A list decoding algorithm is presented for [ ] Reed–Solomon (RS) codes over GF ( ), which is capable of correcting more than ( ) 2 errors. Based on a previous work of Sudan, an extended key equation (EKE) is derived for RS codes, which reduces to the classical key equation when the number of errors is limited to ( ) 2 . Generalizing Massey’s algorithm that finds the shortest recurrence that gen...
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A list decoding algorithm is presented for n k Reed Solomon RS codes over GF q which is capable of correcting more than b n k c errors Based on a previous work of Sudan an extended key equation EKE is derived for RS codes which reduces to the classi cal key equation when the number of errors is limited to b n k c Generalizing Massey s algorithm that nds the shortest recurrence that generates a ...
متن کاملCounting generalized Reed-Solomon codes
In this article we count the number of [n, k] generalized Reed– Solomon (GRS) codes, including the codes coming from a non-degenerate conic plus nucleus. We compare our results with known formulae for the number of [n, 3] MDS codes with n = 6, 7, 8, 9.
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ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 1995
ISSN: 1071-5797
DOI: 10.1006/ffta.1995.1035