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Invited Talk: Decoding Cyclic Codes: The Cooper Philosophy

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Mathematical Methods in Computer Science

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5393))

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Abstract

In 1990, Cooper [9, 10] suggested to use Gröbner basis [3, 4] computation in order to deduce error locator polynomials of cyclic codes.

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References

  1. Augot, D., Bardet, M., Faugere, J.C.: Efficient decoding of (binary) cyclic codes above the correction capacity of the code using Gröbner bases. In: Proc. IEEE Int. Symp. Information Theory 2003 (2003)

    Google Scholar 

  2. Augot, D., Bardet, M., Faugere, J.C.: On formulas for decoding binary cyclic codes. In: Proc. IEEE Int. Symp. Information Theory 2007 (2007)

    Google Scholar 

  3. Buchberger, B.: Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal, Ph. D. Thesis, Innsbruck (1965)

    Google Scholar 

  4. Buchberger, B.: Ein algorithmisches Kriterium für die Lösbarkeit eines algebraischen Gleichungssystems. Aeq. Math. 4, 374–383 (1970)

    Article  MATH  Google Scholar 

  5. Caboara, M.: The Chen-Reed-Helleseth-Truong Decoding Algorithm and the Gianni-Kalkbrenner Gröbner Shape Theorem. J. AAECC 13 (2002)

    Google Scholar 

  6. Chen, X., Reed, I.S., Helleseth, T., Truong, K.: Use of Gröbner Bases to Decode Binary Cyclic Codes up to the True Minimum Distance. IEEE Trans. on Inf. Th. 40, 1654–1661 (1994)

    Article  MATH  Google Scholar 

  7. Chen, X., Reed, I.S., Helleseth, T., Truong, K.: General Principles for the Algebraic Decoding of Cyclic Codes. IEEE Trans. on Inf. Th. 40, 1661–1663 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  8. Chen, X., Reed, I.S., Helleseth, T., Truong, K.: Algebraic decoding of cyclic codes: A polynomial Ideal Point of View. Contemporary Mathematics 168, 15–22 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  9. Cooper III, A.B.: Direct solution of BCH decoding equations. In: Arikan, E. (ed.) Communication, Control and Singal Processing, pp. 281–286. Elsevier, Amsterdam (1990)

    Google Scholar 

  10. Cooper III, A.B.: Finding BCH error locator polynomials in one step. Electronic Letters 27, 2090–2091 (1991)

    Article  MATH  Google Scholar 

  11. Giorgetti, M., Sala, M.: A commutative algebra approach to linear codes, BCRI preprint, 58, UCC Cork, Ireland (2006), www.bcri.ucc.ie

  12. Loustaunau, P., York, E.V.: On the decoding of cyclic codes using Gröbner bases. J. AAECC 8, 469–483 (1997)

    Article  MATH  Google Scholar 

  13. Orsini, E., Sala, M.: Correcting errors and erasures via the syndrome variety. J. Pure Appl. Algebra 200, 191–226 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  14. Orsini, E., Sala, M.: General error locator polynomials for binary cyclic codes with t ≤ 2 and n < 63. IEEE Trans. Inform. Theory 53, 1095–1107 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  15. Orsini, E., Sala, M.: General error locator polynomials for binary cyclic codes with t ≤ 2 and n < 63, BCRI preprint (2005), http://www.bcri.ucc.ie

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Mora, T., Orsini, E. (2008). Invited Talk: Decoding Cyclic Codes: The Cooper Philosophy. In: Calmet, J., Geiselmann, W., Müller-Quade, J. (eds) Mathematical Methods in Computer Science. Lecture Notes in Computer Science, vol 5393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89994-5_10

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  • DOI: https://doi.org/10.1007/978-3-540-89994-5_10

  • Publisher Name: Springer, Berlin, Heidelberg

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