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Coding Theory and Applications pp 77–86Cite as

On the Error-Correcting Radius of Folded Reed–Solomon Code Designs

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Part of the book series: CIM Series in Mathematical Sciences ((CIMSMS,volume 3))

Abstract

A general formula for the error-correcting radius of linear-algebraic multivariate interpolation decoding of folded Reed–Solomon (FRS) codes is derived. Based on this result, an improved construction of FRS codes is motivated, which can be obtained by puncturing Parvaresh–Vardy codes. The proposed codes allow decoding for all rates, remove the structural loss in decoding radius of the original FRS design and maximize the fraction of correctable errors.

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Acknowledgements

The author is supported by the German Ministry of Education and Research in the framework of the Alexander von Humboldt-Professorship and thanks G. Kramer, F. Kschi-schang, and V. Sidorenko as well as C. Senger, H. Bartz for their comments and discussions.

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Authors and Affiliations

  1. Institute for Communications Engineering, Technische Universität München, Munich, Germany

    Joschi Brauchle

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  1. Joschi Brauchle
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Correspondence to Joschi Brauchle .

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Editors and Affiliations

  1. Department of Mathematics, University of Aveiro, Aveiro, Portugal

    Raquel Pinto

  2. Department of Electrical and Computer Engineering, University of Porto, Porto, Portugal

    Paula Rocha Malonek

  3. Department of Mathematics, University of Aveiro, Aveiro, Portugal

    Paolo Vettori

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Brauchle, J. (2015). On the Error-Correcting Radius of Folded Reed–Solomon Code Designs. In: Pinto, R., Rocha Malonek, P., Vettori, P. (eds) Coding Theory and Applications. CIM Series in Mathematical Sciences, vol 3. Springer, Cham. https://doi.org/10.1007/978-3-319-17296-5_7

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