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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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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DOI: https://doi.org/10.1007/978-3-319-17296-5_7
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-17295-8
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