Michael E. O'Sullivan

Research Interests

  • Algebraic Geometry Codes
  • Decoding Algorithms
  • Low-Density Parity-Check Codes
  • Ring-linear Codes
  • Computational Algebraic Geometry
  • Algebraic Curves and Surfaces
  • Algebraic Statistics

Book Chapter

    M. Bras-Amoros, M. E. O'Sullivan, "The Key Equation for One-Point Codes," Chapter 3, pp. 99-152, of Advances in Algebraic Geometry Codes, E. Martinez-Moro, C. Munuera, D. Ruano (eds.), World Scientific, 2008

Articles Submitted to Refereed Journals

  1. K. Lee, M. E. O'Sullivan, ``Algebraic Soft-Decision Decoding of Hermitian Codes'' submitted to IEEE Transaction on Information Theory. arXiv:0807.4995

Articles in Refereed Journals

  1. Kwankyu Lee, Michael E. O'Sullivan, "List Decoding of Hermitian Codes using Groebner Bases" to appear Journal of Symbolic Computation arXiv:cs/0610132
  2. Kwankyu Lee, Michael E. O'Sullivan, "Sudan's List Decoding of Reed-Solomon Codes from a Groebner Basis Perspective," Journal of Symbolic Computation 43 (2008), no. 9, 645--658. arXiv:cs/0601022
  3. M. Bras-Amoros, M. E. O'Sullivan, "Redundancies of Correction-Capability-Optimized Reed-Muller Codes," Discrete Applied Mathematics 156 (2008), no. 15, 3005-3010. arXiv:cs/0609160
  4. M. Bras-Amoros, M. E. O'Sullivan, "Duality for Several Families of Evaluation Codes," Advances in the Mathematics of Communications, 2 (2008), no. 1, 15--33. arXiv:cs/0609159
  5. M. Bras-Amoros, M. E. O'Sullivan, "The Order Bound on the Minimum Distance of the One-Point Codes Associated to a Garcia-Stichtenoth Tower of Function Fields," IEEE Transactions on Information Theory, 53, (2007), no. 11, 4241-4245. arXiv:cs/0609161
  6. M. Bras-Amoros, M. E. O'Sullivan, ``On Semigroups Generated by Two Consecutive Integers and Improved Hermitian Codes," IEEE Transactions on Information Theory, 53 (2007), no. 7, 2560--2566.
  7. E. Byrne, M. Greferath, M. E. O'Sullivan, ``The Linear Programming Bound for Codes over Finite Frobenius Rings,'' Designs, Codes and Cryptography 42 (2007), no. 3, 289--301.
    E. Byrne, M. E. O'Sullivan, M. Greferath, ``Errata for: `The linear programming bound for codes over finite Frobenius rings' '' Designs, Codes, Cryptography, 45 (2007), no. 2, 269--270.
  8. M. Greferath, G. McGuire, M. E. O'Sullivan, ``On Plotkin Optimal Codes over Finite Frobenius Rings,'' Journal of Algebra and Its Applications 5 (2006), no. 6, 799--815.
  9. M. Bras-Amoros, M. E. O'Sullivan, ``The Correction Capability of the Berlekamp-Massey-Sakata Algorithm with Majority Voting,'' Applicable Algebra in Engineering, Communications and Computing 17 (2006), no. 5, 315--335.
  10. M. E. O'Sullivan, ``Algebraic Construction of Sparse Matrices with Large Girth,'' IEEE Transactions on Information Theory, vol. 52, pp. 718-727, 2006.
  11. M. Greferath, M. E. O'Sullivan, "On Bounds for Codes over Frobenius Rings under Homogeneous Weights," Discrete Mathematics, vol. 289, pp. 11-24, 2004.
  12. M. E. O'Sullivan, ``On Koetter's Algorithm and the Computation of Error Values,'' Designs, Codes and Cryptography, vol. 31, pp. 169-188, 2004. ps.gz file
  13. M. E. O'Sullivan, ``The Key Equation for One-Point Codes and Efficient Error Evaluation'' Journal of Pure and Applied Algebra, vol. 169, issue 2-3, pp. 295-320, 2002. ps.gz file
  14. M. E. O'Sullivan, ``New Codes for the Berlekamp-Massey-Sakata Algorithm,'' Finite Fields and Their Applications, vol. 7, pp. 293-317, 2001.
  15. M. E. O'Sullivan, ``Decoding of Hermitian Codes: The Key Equation and Efficient Error Evaluation,'' IEEE Transactions on Information Theory, vol. 46, no. 2, pp. 512-523, 2000.
  16. M. E. O'Sullivan, ``Decoding of Codes Defined by a Single Point on a Curve,'' IEEE Transactions on Information Theory, special issue on algebraic geometry codes, vol. 41, no. 6, pp. 1709-1719, 1995.

Articles in Refereed Proceedings

  1. M. Bras-Amoros, M. E. O'Sullivan, ``Extended Norm-Trace Codes with Optimized Correction Capability,'' Lecture Notes in Computer Science, Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, P. V. Kumar, T. Hoholdt, H. Janwa (eds.), Springer, vol. 4851, pp. 337-346, Dec., 2007.
  2. M. O'Sullivan, J. Brevik, R. Wolski, "The Sum-Product Algorithm on Small Graphs," in Advances in Coding Theory and Cryptology, T. Shaska, W. C. Huffman, D. Joyner, V. Ustimenko eds., Series on Coding Theory and Cryptology, 2. World Scientific, 2007, 160-180.
  3. E. Byrne, M. Greferath, M. E. O'Sullivan, ``Duality of Ring-Linear Codes and a Linear Programming Bound,'' International Workshop on Coding and Cryptography, Versailles, France, 2007.
  4. R. Agarwal, E. Popovici, B. O'Flynn, M. O'Sullivan, "A Parallel Architecture for Hermitian Decoders: Satisfying Resource and Throughput Constraints," IEEE Proc., International Symposium on Circuits and Systems, ISCAS 2007.
  5. R. Moberly, M. O'Sullivan and K. Waheed, ``LDPC Decoder with a Limited-Precision FPGA-based Floating-Point Multiplication Coprocessor,'' Proceedings SPIE Advanced Signal Processing Algorithms, Architectures, and Implementations, August 2007.
  6. R. Moberly, M. O'Sullivan, ``Representing Probabilities with Limited Precision for Iterative Soft-Decision LDPC Decoding'', Proceedings Wireless and Personal Multimedia Conference, September 2006.
  7. R. Moberly, M. O'Sullivan, ``Computational Performance of Various Formulations of the Iterative Soft-Decision Decoder Algorithm'', Proceedings IEEE International Symposium on Information Theory, Seattle, WA, July, 2006, pp. 1703-1707.
  8. K. Lee, M. E.O'Sullivan Groebner Bases for Soft-Decision Decoding of Reed-Solomon Codes 2006 IEEE International Symposium on Information Theory, Seattle, WA, July, 2006, pp. 2032--2036.
  9. M. E. O'Sullivan, J. Brevik, R. Wolski ``The Performance of LDPC codes with Large Girth,'' Proc. 43rd Allerton Conference on Communication, Control and Computing, Univ. Illinois, 2005, pp. 1759-1767.
  10. A. Byrne, E. Popovici, M. E. O'Sullivan, ``Versatile Architectures for Decoding a Class of LDPC Codes,'' IEEE European Conference on Circuit Theory and Design 2005, to appear.
  11. M. Greferath, M. E. O'Sullivan, R. Smarandache, ``Construction of Good LDPC Codes using Dilation Matrices,'' Proc. IEEE International Symposium on Information Theory, Chicago, Illinois, p. 237, 2004.
  12. M. E. O'Sullivan, R. Smarandache, ``High-rate, Short Length, (3, 3s)-regular LDPC Codes of Girth 6 and 8,'' Proc. IEEE International Symposium on Information Theory, Yokohama, Japan, p. 59, 2003.
  13. M. E. O'Sullivan, M. Greferath, R. Smarandache, "Construction of LDPC Codes from Affine Permutation Matrices," Proc. 40th annual Allerton Conference of Communication, Control and Computing, Univ. Illinois, 2002. ps.gz file
  14. E. Popovici, P. Fitzpatrick, R. Koetter, M. E. O'Sullivan, ``Implementation of a Hermitian decoder,'' in Proc. IEEE Int. Symp. Information Theory , Washington D. C., p. 311, July 2001.
  15. M. E. O'Sullivan, ``Alternative Approaches to the Computation of Error Values for Hermitian Codes,'' Proceedings of the 37th Allerton Conference on Communication, Control and Computing, Univ. Illinois, pp 557-566, 2000. ps.gz file
  16. M. E. O'Sullivan, ``Decoding of Codes on Surfaces,'' Proc., IEEE Information Theory Workshop, Killarney, Ireland, pp. 33-34, June, 1998.
  17. M. E. O'Sullivan, ``Decoding of One-Point Codes Using Error Evaluator Polynomials,'' Proc. IEEE International Symposium on Information Theory, Ulm, Germany, p. 377, July 1997.
  18. M. E. O'Sullivan, ``Decoding Hermitian Codes Beyond (d-1)/2'' Proc. IEEE International Symposium on Information Theory, Ulm, Germany, p. 384, July 1997.
  19. M. E. O'Sullivan, ``VLSI Architecture for a Decoder for Hermitian Codes'' Proc. IEEE International Symposium on Information Theory, Ulm, Germany, p. 376, July 1997.

Short Courses

  1. Lecturer, Soria Summer School on Computational Mathematics: Algebraic Coding Theory, Soria, Spain, July 2-11, 2008.
  2. Lecturer, 2004 Summer Program for Graduate Students in Coding and Cryptography, sponsored by the Institute for Mathematics and Its Applications, University of Notre Dame, June 8-26, 2004.
  3. Short course: ``Coding Theory: Code Constructions and Algorithms'' Universitat Politecnica de Catalunya, Barcelona, Spain, June 2-6, 2003.

Unpublished Articles

  • ``Decoding of Hermitian Codes: Beyond the Minimum Distance Bound,'' manuscript. ps.gz file
  • ``A Generalization of the Berlekamp-Massey-Sakata Algorithm'' manuscript. ps.gz file
    • DEC.