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On decoding of Reed-Solomon codes
IEEE Transactions on Information Theory, 1971It is shown how nonsystematic Reed-Solomon (RS) codes encoded by means of the Chinese remainder theorem can be decoded using the Berlekamp algorithm. The Chien search and calculation of error values are not needed but are replaced by a polynomial division and added calculation in determining the syndrome.
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1999
In December of 1958 I. S. Reed and G. Solomon finished the report, entitled “polynomial codes over certain finite fields” at the M.I.T Lincoln Laboratory [1]. In 1960, a slight modification of this report was published as a paper [2] in the Journal of the Society for Industrial and Applied Mathematics(SIAM).
Irving S. Reed, Xuemin Chen
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In December of 1958 I. S. Reed and G. Solomon finished the report, entitled “polynomial codes over certain finite fields” at the M.I.T Lincoln Laboratory [1]. In 1960, a slight modification of this report was published as a paper [2] in the Journal of the Society for Industrial and Applied Mathematics(SIAM).
Irving S. Reed, Xuemin Chen
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Asymmetric quantum Reed-Solomon and generalized Reed-Solomon codes
Quantum Information Processing, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Chinese Annals of Mathematics, Series B, 2010
The complexity of decoding the standard Reed-Solomon code is a well-known open problem in coding theory. This two-part paper addresses this problem. In the first part, the author improves known upper bounds for the error distance of a received word to a Reed-Solomon code over \(\text{GF}(q)\).
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The complexity of decoding the standard Reed-Solomon code is a well-known open problem in coding theory. This two-part paper addresses this problem. In the first part, the author improves known upper bounds for the error distance of a received word to a Reed-Solomon code over \(\text{GF}(q)\).
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1994
The purpose of this chapter is to give an overview of Reed-Solomon (RS) codes [67] as an important subclass of nonbinary Bose-Chaudhuri-Hocquenghem (BCH) codes. Our aim is in this chapter to cover the background which is required for the forthcoming sections related to RS codes.
S. Hamidreza Jamali, Tho Le-Ngoc
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The purpose of this chapter is to give an overview of Reed-Solomon (RS) codes [67] as an important subclass of nonbinary Bose-Chaudhuri-Hocquenghem (BCH) codes. Our aim is in this chapter to cover the background which is required for the forthcoming sections related to RS codes.
S. Hamidreza Jamali, Tho Le-Ngoc
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On the concatenation of turbo codes and Reed-Solomon codes
IEEE International Conference on Communications, 2003. ICC '03., 2004This paper studies the concatenation of turbo codes and Reed-Solomon (RS) codes. The error patterns of turbo codes are first analyzed. Since error patterns of turbo codes are much different than those of convolutional codes, the design rules for a matched interleaver between turbo codes and RS codes are provided.
Guangcai Zhou +6 more
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Hermitian codes as generalized Reed-Solomon codes
Designs, Codes and Cryptography, 1992zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tomik Yaghoobian, Ian F. Blake
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2019
In this chapter, we will give information about Reed-Solomon codes. These codes fall into the category of nonbinary cyclic codes. The generator polynomials of Reed-Solomon codes are constructed using the minimal polynomials of the extended finite fields. Reed-Solomon codes are effective for burst errors and they are used for erasure decoding.
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In this chapter, we will give information about Reed-Solomon codes. These codes fall into the category of nonbinary cyclic codes. The generator polynomials of Reed-Solomon codes are constructed using the minimal polynomials of the extended finite fields. Reed-Solomon codes are effective for burst errors and they are used for erasure decoding.
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2003
Die Reed-Solomon-Codes (RS-Codes) sind eine besonders wichtige Klasse von linearen Codes, die haufig in der Praxis benutzt werden. Thematisch gehoren sie eigentlich als eine spezielle Form der BCH-Codes in Kapitel 3. Wegen ihrer grosen praktischen Bedeutung wollen wir ihnen jedoch ein eigenes Kapitel widmen.
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Die Reed-Solomon-Codes (RS-Codes) sind eine besonders wichtige Klasse von linearen Codes, die haufig in der Praxis benutzt werden. Thematisch gehoren sie eigentlich als eine spezielle Form der BCH-Codes in Kapitel 3. Wegen ihrer grosen praktischen Bedeutung wollen wir ihnen jedoch ein eigenes Kapitel widmen.
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2001
So far, we’ve looked at bit-oriented error correcting schemes. Reed-Solomon (RS) codes, however, are symbol-based. In other words, bits are combined into symbols upon which the coding is performed. RS codes are a special example of a more general class of block codes called BCH codes after Bose, Chaudhuri and Hocquenghem, forefathers of the theory ...
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So far, we’ve looked at bit-oriented error correcting schemes. Reed-Solomon (RS) codes, however, are symbol-based. In other words, bits are combined into symbols upon which the coding is performed. RS codes are a special example of a more general class of block codes called BCH codes after Bose, Chaudhuri and Hocquenghem, forefathers of the theory ...
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