Michael O'Sullivan

Michael O'Sullivan

Professor of Mathematics
Department of Mathematics and Statistics
Center for Research in Mathematics and Science Education

Email

Primary Email: [email protected]

Building/Location

Geology Mathematics Computer Science - 579

Website Links

Areas of Specialization

Research Interests (roughly in reverse chronologically)

    • Algebraic Statistics: This is my current passion.
      • The geometry of the space of entropy vectors for n random variables (the entropic polymatroids).
      • The combinatorics of probabilistic models: graphoids, semigraphoids and such.
      • Bayesian Reasoning on directed acyclic graphs, and generalizations to other probablistic models.
    • Algebraic Geometry Codes and Decoding
      • Dimension and minimum distance for codes from curves and other varieties.
      • Decoding algorithms that generalize the Berlekamp-Massey algorithm.
      • Interpolation decoding using Groebner basis techniques following Sudan's list-decoding breakthrough.
    • Low-Density Parity-Check Codes
      Creation of good LDPC codes using basic number theory.
      Analysis of the sum-product algorithm.
  • Ring-linear Codes
    • Bounds for ring-linear codes generalizing MacWilliams work.
  • Algebraic Curves and Surfaces
    Graduate studies on linkage theory and generalized divisors on Gorenstein curves.
    My thesis was on divisor classes on normal cubic surfaces.

Grants

Research Grants

  1. National Science Foundation, Directorate for Computer and Information Science and Engineering, "Decoding of Algebraic Geometry Codes: Theoretical Analysis, Efficient Algorithms, Practical Implementation," PI: M. E. O'Sullivan (7/2009).
  2. National Science Foundation, Directorate for Computer and Information Science and Engineering, "Collaborative Research: Improving Low-Density Parity-Check Codes Through Algebraic Analysis of the Sum-Product Algorithm," PIs: M. E. O'Sullivan, J. Brevik (CSULB), R. Wolski (UCSB) (2/2007).
  3. Korea Research Foundation, Postdoctoral Foreign Study Grant, PI M. E. O'Sullivan. Supported one-year postdoctoral position for Kwankyu Lee (7/2005-6/2006).
  4. National Science Foundation, Division of Networking and Communication Research and Infrastructure: "High-Performance Decoding of Algebraic Codes beyond their Packing Radii," PI R. Blahut (UIUC) (8/2000-7/2003). I was an investigator.
  5. National Science Foundation, Division of Networking and Communication Research and Infrastructure grant, "Implementation and Applications of Practical Codes on Curves," PI R. Blahut (UIUC), Co-PI M. E. O'Sullivan, (7/1998-6/2000).
  6. National Science Foundation, Small Business Innovations Research Grant, "Construction of a Decoder for an Algebraic Geometry Code," PI M. E. O'Sullivan. Phase I (2/1993-10/1993) and Phase II (7/1994-9/1996).
  7. Department of Energy, Small Business Cooperative Research and Development Grant (9/1994-12/1994): Joint work with the Computer Research Group at the Lawrence Livermore National Laboratory.

Educational Grants

  1. SDSU President's Leadership Fund, "A Discrete Mathematics Problem Library for Online Homework," PI: M. E. O'Sullivan, CoPI: Tom Schmidt (2012).
  2. SDSU President's Leadership Fund, "Incorporating Computational Software into Mathematics Courses," PI: M. E. O'Sullivan, coPI: David Monarres (2009).
  3. SDSU Travel grant, "Research Collaboration in Applied Algebra with the National University of Ireland." (5-6/2004).

Publications

K. Lee, M. Bras-Amoros, M. E. O'Sullivan, "Unique decoding of general AG codes," IEEE Transactions on Information Theory, 60 (2014),no. 4, pp. 2038-2053.arXiv:1210.3101

F. Hernando, M.E. O'Sullivan,D. Ruano, "List decoding of repeated codes," Applicable Algebra in Engineering, Communications and Computing, 24 (2013), no. 3-4, pp. 237-253. arXiv:1202.1238

F. Hernando, K. Marshall, M. E. O'Sullivan, "The dimension of subcode-subfields of shortened generalized Reed-Solomon codes," Designs, Codes, Cryptography, 69 (2013), pp. 131-142. arXiv:1108.5475

K. Lee, M. Bras-Amoros, M. E. O'Sullivan, "Unique decoding of plane AG codes via interpolation." IEEE Transactions on Information Theory 58 (2012), no. 6, pp. 3941-3950. arXiv:1110.6251

K. Lee, M. E. O'Sullivan, "Algebraic Soft-Decision Decoding of Hermitian Codes" IEEE Transaction on Information Theory 56 (2010) no. 6, pp. 2587-2600. arXiv:0807.4995

K. Lee, M. E. O'Sullivan, "List Decoding of Hermitian Codes using Groebner Bases" Journal of Symbolic Computation, 40 (2009) 12, 1662-1675. arXiv:cs/0610132

K. Lee, M. 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

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

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

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

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. arXiv:cs/0609162

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.

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.