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JOURNALS // Izvestiya of Saratov University. Mathematics. Mechanics. Informatics

Izv. Saratov Univ. Math. Mech. Inform., 2022, Volume 22, Issue 1, Pages 28–47 (Mi isu920)

Decoding algorithms for Goppa codes with errors and erasures
S. M. Ratseev, O. I. Cherevatenko

References

1. Status Report on the First Round of the NIST Post-Quantum Cryptography Standardization Process. National Institute of Standards and Technology. Internal Report 8240, January 2019, 27 pp.  crossref
2. Goppa V. D., “A New Class of Linear Correcting Codes”, Problems of Information Transmission, 6:3 (1970), 207–212  mathnet  mathscinet  zmath
3. MacWilliams F. J., Sloane N. J. A., The Theory of Error Correcting Codes, North-Holland Pub. Co, Amsterdam–New York, 1977, 762 pp.  mathscinet  zmath
4. Blahut R. E., Theory and Practice of Error Control Codes, Addison-Wesley Pub. Co, Reading, Mass., 1983, 500 pp.  mathscinet  mathscinet  zmath
5. Gao S., “A new algorithm for decoding Reed–Solomon codes”, Communications, Information and Network Security, 712, eds. V. Bhargava, H. V. Poor, V. Tarokh, S. Yoon, Kluwer, Norwell, MA, 2003, 55–68  crossref
6. Huffman W. C., Pless V., Fundamentals of Error-Correcting Codes, Cambridge University Press, New York–Cambridge, 2003, 646 pp.  mathscinet  zmath
7. Ratseev S. M., Elements of Higher Algebra and Coding Theory, Lan', St. Petersburg, 2022, 656 pp. (in Russian)
8. Fedorenko S. V., “Simple algorithm for decoding algebraic codes”, Information and Control Systems, 2008, no. 3, 23–27 (in Russian)
9. Gohberg I., Olshevsky V., “The fast generalized Parker–Traub algorithm for inversion of Vandermonde and related matrices”, Journal of Complexity, 13:2 (1997), 208–234  crossref  mathscinet  zmath  scopus
10. Yan S., Yang A., “Explicit algorithm to the inverse of Vandermonde matrix”, 2009 International Conference on Test and Measurement (Hong Kong, 2009), 176–179  crossref  scopus
11. Rawashdeh E. A., “A simple method for finding the inverse matrix of Vandermonde matrix”, MATEMATIC̆KI VESNIK, 71:3 (2019), 207–213  mathscinet  zmath
12. Ratseev S. M., Cherevatenko O. I., “On decoding algorithms for generalized Reed–Solomon codes with errors and erasures”, Vestnik of Samara University. Natural Science Series, 26:3 (2020), 17–29 (in Russian)  mathnet  crossref  mathscinet


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