On the error distance of extended Reed-Solomon codes | Zendy

YuJuan Li | Zendy; Guizhen Zhu | Zendy

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On the error distance of extended Reed-Solomon codes

Author(s) -

YuJuan Li,

Guizhen Zhu

Publication year - 2016

Publication title -

advances in mathematics of communications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.601

H-Index - 26

eISSN - 1930-5346

pISSN - 1930-5338

DOI - 10.3934/amc.2016015

Subject(s) - reed–solomon error correction , mathematics , corollary , minimum distance , decoding methods , reed–muller code , algebraic number , error detection and correction , list decoding , word (group theory) , concatenated error correction code , arithmetic , combinatorics , discrete mathematics , block code , algorithm , geometry , mathematical analysis

It is well known that the main problem of decoding the extended Reed-Solomon codes is computing the error distance of a word. Using some algebraic constructions, we are able to determine the error distance of words whose degrees are $k+1$ and $k+2$ to the extended Reed-Solomon codes. As a corollary, we can simply get the results of Zhang-Fu-Liao on the deep hole problem of Reed-Solomon codes.

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