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Polynomial Codes Over Certain Finite Fields

I.S. Reed, G. Solomon

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Previous article Next article Polynomial Codes Over Certain Finite FieldsI. S. Reed and G. SolomonI. S. Reed and G. Solomonhttps://doi.org/10.1137/0108018PDFPDF PLUSBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] R. W. Hamming, Error detecting and error correcting codes, Bell System Tech. J., 29 (1950), 147–160 MR0035935 CrossrefISIGoogle Scholar[2] Irving S. Reed, A class of multiple-error-correcting codes and the decoding scheme, Trans. I.R.E., PGIT-4 (1954), 38–49, Prof. Group on Information Theory MR0089789 Google Scholar[3] Neal Zierler, Linear recurring sequences, J. Soc. Indust. Appl. Math., 7 (1959), 31–48 10.1137/0107003 MR0101979 0096.33804 LinkISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails A General Family of MSRD Codes and PMDS Codes with Smaller Field Sizes from Extended Moore MatricesUmberto MartÍnez-Pen͂asSIAM Journal on Discrete Mathematics, Vol. 36, No. 3 | 16 August 2022AbstractPDF (562 KB)Algorithmic Fault Tolerance Using the Lanczos MethodSIAM Journal on Matrix Analysis and Applications, Vol. 13, No. 1 | 31 July 2006AbstractPDF (1962 KB)A New Class of Cyclic CodesSIAM Journal on Applied Mathematics, Vol. 16, No. 1 | 12 July 2006AbstractPDF (1580 KB)Multiple-Burst Error Correction with the Chinese Remainder TheoremJournal of the Society for Industrial and Applied Mathematics, Vol. 11, No. 1 | 13 July 2006AbstractPDF (758 KB)A Class of Error-Correcting Codes in $p^m $ SymbolsDaniel Gorenstein and Neal ZierlerJournal of the Society for Industrial and Applied Mathematics, Vol. 9, No. 2 | 10 July 2006AbstractPDF (691 KB) Volume 8, Issue 2| 1960Journal of the Society for Industrial and Applied Mathematics225-424 History Submitted:21 January 1959Published online:10 July 2006 InformationCopyright © 1960 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0108018Article page range:pp. 300-304ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics

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Previous article Next article Polynomial Codes Over Certain Finite FieldsI. S. Reed and G. SolomonI. S. Reed and G. Solomonhttps://doi.org/10.1137/0108018PDFPDF PLUSBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] R. W. Hamming, Error detecting and error correcting codes, Bell System Tech. J., 29 (1950), 147–160 MR0035935 CrossrefISIGoogle Scholar[2] Irving S. Reed, A class of multiple-error-correcting codes and the decoding scheme, Trans. I.R.E., PGIT-4 (1954), 38–49, Prof. Group on Information Theory MR0089789 Google Scholar[3] Neal Zierler, Linear recurring sequences, J. Soc. Indust. Appl. Math., 7 (1959), 31–48 10.1137/0107003 MR0101979 0096.33804 LinkISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails A General Family of MSRD Codes and PMDS Codes with Smaller Field Sizes from Extended Moore MatricesUmberto MartÍnez-Pen͂asSIAM Journal on Discrete Mathematics, Vol. 36, No. 3 | 16 August 2022AbstractPDF (562 KB)Algorithmic Fault Tolerance Using the Lanczos MethodSIAM Journal on Matrix Analysis and Applications, Vol. 13, No. 1 | 31 July 2006AbstractPDF (1962 KB)A New Class of Cyclic CodesSIAM Journal on Applied Mathematics, Vol. 16, No. 1 | 12 July 2006AbstractPDF (1580 KB)Multiple-Burst Error Correction with the Chinese Remainder TheoremJournal of the Society for Industrial and Applied Mathematics, Vol. 11, No. 1 | 13 July 2006AbstractPDF (758 KB)A Class of Error-Correcting Codes in $p^m $ SymbolsDaniel Gorenstein and Neal ZierlerJournal of the Society for Industrial and Applied Mathematics, Vol. 9, No. 2 | 10 July 2006AbstractPDF (691 KB) Volume 8, Issue 2| 1960Journal of the Society for Industrial and Applied Mathematics225-424 History Submitted:21 January 1959Published online:10 July 2006 InformationCopyright © 1960 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0108018Article page range:pp. 300-304ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics

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Previous article Next article Polynomial Codes Over Certain Finite FieldsI. S. Reed and G. SolomonI. S. Reed and G. Solomonhttps://doi.org/10.1137/0108018PDFPDF PLUSBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] R. W. Hamming, Error detecting and error correcting codes, Bell System Tech. J., 29 (1950), 147–160 MR0035935 CrossrefISIGoogle Scholar[2] Irving S. Reed, A class of multiple-error-correcting codes and the decoding scheme, Trans. I.R.E., PGIT-4 (1954), 38–49, Prof. Group on Information Theory MR0089789 Google Scholar[3] Neal Zierler, Linear recurring sequences, J. Soc. Indust. Appl. Math., 7 (1959), 31–48 10.1137/0107003 MR0101979 0096.33804 LinkISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails A General Family of MSRD Codes and PMDS Codes with Smaller Field Sizes from Extended Moore MatricesUmberto MartÍnez-Pen͂asSIAM Journal on Discrete Mathematics, Vol. 36, No. 3 | 16 August 2022AbstractPDF (562 KB)Algorithmic Fault Tolerance Using the Lanczos MethodSIAM Journal on Matrix Analysis and Applications, Vol. 13, No. 1 | 31 July 2006AbstractPDF (1962 KB)A New Class of Cyclic CodesSIAM Journal on Applied Mathematics, Vol. 16, No. 1 | 12 July 2006AbstractPDF (1580 KB)Multiple-Burst Error Correction with the Chinese Remainder TheoremJournal of the Society for Industrial and Applied Mathematics, Vol. 11, No. 1 | 13 July 2006AbstractPDF (758 KB)A Class of Error-Correcting Codes in $p^m $ SymbolsDaniel Gorenstein and Neal ZierlerJournal of the Society for Industrial and Applied Mathematics, Vol. 9, No. 2 | 10 July 2006AbstractPDF (691 KB) Volume 8, Issue 2| 1960Journal of the Society for Industrial and Applied Mathematics225-424 History Submitted:21 January 1959Published online:10 July 2006 InformationCopyright © 1960 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0108018Article page range:pp. 300-304ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics

Key concepts: Reed–Solomon error correction, Finite field, Hamming code, Hamming distance, Coding theory, Mathematics, BCH code, Discrete mathematics

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