Michael E. O'Sullivan

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

Articles Submitted to Refereed Journals

• Kwankyu Lee, Michael E. O'Sullivan, "List Decoding of Hermitian Codes using Groebner Bases" submitted to Journal of Symbolic Computation arXiv:cs/0610132
• Kwankyu Lee, Michael E. O'Sullivan, " Sudan's List Decoding of Reed-Solomon Codes from a Groebner Basis Perspective" submitted to Journal of Symbolic Computation arXiv:cs/0601022
• M. Bras-Amoros, M. E. O'Sullivan, "Redundancies of Correction-Capability-Optimized Reed-Muller Codes" submitted to Discrete Applied Mathematics arXiv:cs/0609160
• M. Bras-Amoros, M. E. O'Sullivan, "Duality for Several Families of Evaluation Codes" arXiv:cs/0609159

Articles in Refereed Journals

• 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, to appear, Nov. 2007. arXiv:cs/0609161
• M. Bras-Amoros, M. E. O'Sullivan, ``On Semigroups Generated by Two Consecutive Integers and Improved Hermitian Codes," IEEE Transactions on Information Theory, to appear July, 2007.
• E. Byrne, M. Greferath, M. E. O'Sullivan, ``The Linear Programming Bound for Codes over Finite Frobenius Rings,'' to appear in Designs, Codes and Cryptography.
• 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.
• 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.
• M. E. O'Sullivan, ``Algebraic Construction of Sparse Matrices with Large Girth,'' IEEE Transactions on Information Theory, vol. 52, pp. 718-727, 2006.
• M. Greferath, M. E. O'Sullivan, "On Bounds for Codes over Frobenius Rings under Homogeneous Weights," Discrete Mathematics, vol. 289, pp. 11-24, 2004.
• 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
  
• 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
• M. E. O'Sullivan, ``New Codes for the Berlekamp-Massey-Sakata Algorithm,'' Finite Fields and Their Applications, vol. 7, pp. 293-317, 2001.
• 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.
• 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

• 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 Publishing Co., 2007.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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
• 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.
• 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
• M. E. O'Sullivan, ``Decoding of Codes on Surfaces,'' Proc., IEEE Information Theory Workshop, Killarney, Ireland, pp. 33-34, June, 1998.
• 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.
• M. E. O'Sullivan, ``Decoding Hermitian Codes Beyond (d-1)/2'' Proc. IEEE International Symposium on Information Theory, Ulm, Germany, p. 384, July 1997.
• 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.

Conferences, Short Courses

• 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.
• Short course: ``Coding Theory: Code Constructions and Algorithms'' Universitat Politecnica de Catalunya, Barcelona, Spain, June 2-6, 2003.
• M. E. O'Sullivan, ``Building Low-density Parity-check Codes with Affine Permutation Matrices,'' 15th Annual Symposium on Mathematical Theory of Networks and Systems, Notre Dame, Aug 12-16, 2002.
• M. E. O'Sullivan, ``Decoding of One-Point Codes with Koetter's Algorithm,'' Conference on Symbolic Computational Algebra, London, Ontario, July, 2002.
• M. E. O'Sullivan, ``Construction of Codes for the Iterative Decoding Algorithm,'' Conference of the Catalan Mathematical Society, Barcelona, Spain, May 2002.
• ``The Key Equation for One-Point Codes,'' Institute for Mathematics and its Applications Summer Workshop, Codes Systems and Graphical Models, Aug. 1999.
• ``Decoding of Algebraic Geometry Codes,'' Colloquium Lecture, University of Notre Dame, September, 1998.
• ``Decoding of codes defined by a ring with an order function,'' Joint Meetings of the AMS-MAA, Baltimore, Maryland, Jan., 1998.
• ``Decoding of One-Point Codes,'' Midwest Algebraic Geometry Conference, Notre Dame, Indiana, Nov. 1997.
• ``The Key Equation for One-Point Codes,'' Workshop on Arithmetic, Geometry and Coding Theory, Luminy, France, June 1997.
• ``Classification and Divisor Class Groups of Normal Cubic Surfaces in P^3'' Eastern Section meeting of the American Mathematical Society, Oct 5, 1996.

Unpublished Articles