On the error distance of extended Reed-Solomon codes

Yujuan  Li; Guizhen  Zhu

doi:10.3934/amc.2016015

Article Contents

2016, Volume 10, Issue 2: 413-427. Doi: 10.3934/amc.2016015

This issue Previous Article Nearly perfect sequences with arbitrary out-of-phase autocorrelation Next Article Coherence of sensing matrices coming from algebraic-geometric codes

On the error distance of extended Reed-Solomon codes

Yujuan Li^1, and
Guizhen Zhu^2,

1.
Science and Technology on Information Assurance Laboratory, Beijing
2.
Data Communication Science and Technology Research Institute, Beijing

Received: September 2014

Revised: November 2015

Published: May 2016

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Abstract

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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Mathematics Subject Classification: 94B35;11C08.

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