General Info:

This page contains some Recent Papers, Preprints and additional material, useful to people in my research area. Most of the papers can be downloaded. Papers are in Postscript and PDF format. Comments and feedback are very welcome.

Recent Papers:

• G. Han and J. Rosenthal. Unitary Space Time Constellation Analysis: An Upper Bound for the Diversity.
  E-print math.CO/0401045 , January 2004.
• G. Han and J. Rosenthal. A Numerical Approach for Designing Unitary Space Time Codes with Large Diversity.
  E-print math.OC/0312170 , December 2003.
• C. Kelley, J. Rosenthal and D. Sridhara. Some new Algebraic constructions of Codes from Graphs which are good Expanders.
  In Proc. of the 41-st Allerton Conference on Communication, Control, and Computing, pages 1280-1289, 2003.
• R. Hutchinson, J. Rosenthal and R. Smarandache. Convolutional Codes with Maximum Distance Profile.
  E-print math.OC/0307196 , July, 2003.
• H. Gluesing-Luerssen, J. Rosenthal and R. Smarandache. Strongly MDS Convolutional Codes.
  E-print math.RA/0303254 , March, 2003.
• G. Han and J. Rosenthal. Unitary Constellations with Large Diversity Sum and Good Diversity Product.
  In Proc. of the 40-th Allerton Conference on Communication, Control, and Computing, pages 48-57, 2002.
• G. Han and J. Rosenthal. Unitary Constellation Design with Application to Space-Time Coding.
  In D. Gilliam and J. Rosenthal editors, Mathematical Theory of Networks and Systems, (12 pages), August 2002.
  Electronic Proceedings MTNS-2002 Symposium held in at the University of Notre Dame.
• G. Han, K. Portman, and J. Rosenthal. Unitary matrices with maximal or near maximal diversity product.
  In Proc. of the 39-th Allerton Conference on Communication, Control, and Computing, pages 82-91, 2001.
• R. Smarandache, H. Gluesing-Luerssen and J. Rosenthal. Constructions of MDS-convolutional codes.
  IEEE Trans. Inform. Theory. 47(5):2045-2049, 2001.
  (PDF file)
• J. Rosenthal. Connections between linear systems and convolutional codes.
  In B. Marcus and J. Rosenthal editors, "Codes, Systems and Graphical Models",
  IMA Vol 123, pages 39-66, Sprinegr Verlag, 2001.
  E-print math.OC/0005281, May 2000.
  (PDF file)
• J. Rosenthal and P. O. Vontobel. Constructions of LDPC codes using Ramanujan graphs and ideas from Margulis.
  In Proc. of the 38-th Annual Allerton Conference on Communication, Control, and Computing, pages 248--257, 2000.
  (PDF file)
• H. Gluesing-Luerssen, J. Rosenthal, and P. A. Weiner. Duality between multidimensional convolutional codes and systems.
  In F. Colonius, U. Helmke, F. Wirth, and D. Praetzel-Wolters, editors, Advances in Mathematical Systems Theory, A Volume in Honor of Diederich Hinrichsen, pages 135--150. Birkhauser, Boston, 2000.
  E-print math.OC/9905046, May 1999.
  (PDF file)
• J. Rosenthal and R. Smarandache. Maximum distance separable convolutional codes
  Applicable Algebra Engrg. Comm. Comput.,
  10(1):15-32, 1999.
  MSRI Preprint #1998-074, December 1998.
  (PDF file)
  

• J. Rosenthal and E.V. York. BCH convolutional codes.
  IEEE Trans. Inform. Theory. 45(6):1833-1844, 1999.
  (PDF file)

• J. Rosenthal. An algebraic decoding algorithm for convolutional codes.
  In G. Picci, D.S. Gilliam, editor, Dynamical Systems, Control, Coding, Computer Vision: New Trends, Interfaces, and Interplay . pages 343--360, Birkäuser, Boston-Basel-Berlin, 1999.
  (PDF file)
  Birkhauser site for book.

• J. Rosenthal. An optimal control theory for systems defined over finite rings.
  In V.D. Blondel, E.D. Sontag, M. Vidyasagar, and J.C. Willems, editors, Open Problems in Mathematical Systems and Control Theory, chapter 38, pages 193-201. Springer-Verlag, London, Berlin, New York, 1998.
  (PDF file)

• R. Smarandache, H. Gluesing-Luerssen, and J. Rosenthal. Generalized first order descriptions and canonical forms for convolutional codes.
  In A.~Beghi, L.~Finesso, and G.~Picci, editors, Mathematical Theory of Networks and Systems, pages 1091--1094, July 1998. Proceedings of the MTNS-98 Symposium held in Padova, Italy.

• R. Smarandache and J. Rosenthal. A state space approach for constructing MDS rate 1/n convolutional codes.
  In Proceedings of the 1998 IEEE Information Theory Workshop on Information Theory, pages 116-117, Killarney, Kerry, Ireland, June 1998.
  (PDF file)

• J. Rosenthal. Some interesting problems in systems theory which are of fundamental importance in coding theory.
  In Proc. of the 36th IEEE Conference on Decision and Control, pages 4574-4579, San Diego, California, 1997.
  (ps.gz file)

• J. Rosenthal and R. Smarandache. Construction of convolutional codes using methods from linear systems theory.
  In Proc. of the 35-th Annual Allerton Conference on Communication, Control, and Computing, pages 953-960, 1997.
  (ps.gz file)

• J. Rosenthal and E. York, On the generalized Hamming weights of convolutional codes.
  IEEE Trans. Inform. Theory. 43(1):330-335, 1997.
  (ps.gz file )
  (PDF file)

• J. Rosenthal,J. M. Schumacher and E.V. York, On behaviors and convolutional codes.
  IEEE Trans. Inform. Theory. 42(6):1881-1891, 1996.
  (ps.gz file)

• G. Maze, C. Monico and J. Rosenthal. Public Key Cryptography based on Semigroup Actions.
  E-print cs.CR/0501017 , January 2005.
• J. C. Interlando, E. Byrne, and J. Rosenthal. The gate complexity of syndrome decoding of Hamming codes.
  In Proceedings of the Tenth International Conference on Applications of Computer Algebra, pages 33-37, Beaumont, Texas, 2004.
• J. Rosenthal. A Polynomial Description of the Rijndael Advanced Encryption Standard.
  Journal of Algebra and its Applications. 2(2):223-236, 2003
  E-print cs.CR/0205002, May 2002.
• G. Maze, C. Monico, J. Climent and J. Rosenthal. Public Key Cryptography based on Simple Modules over Simple Rings.
  In D. Gilliam and J. Rosenthal editors, Mathematical Theory of Networks and Systems, (8 pages), August 2002.
  Electronic Proceedings MTNS-2002 Symposium held in at the University of Notre Dame.

• M. Kim, J. Rosenthal and X. Wang. Pole placement and matrix extension problems: A common point of view
  SIAM J. Control Optim., to appear.

• J. Rosenthal and X. Wang. The multiplicative inverse eigenvalue problem over an algebraically closed field.
  SIAM J. Matrix Anal. Appl. 23(2):517--523, 2001.
  SIAM site for downloading the paper.
  E-print math.RA/0009163, September 2000.
  

• J. Rosenthal and X. Wang. Eigenvalue completions by affine varieties.
  Proc. of AMS. 128(3):643--646, 2000.

• J. Leventides, J. Rosenthal, and X. Wang. The pole placement problem via PI feedback controllers.
  Internat. J. Control, 72(12):1065-1077, 1999.

• J. Rosenthal and J. C. Willems. Open problems in the area of pole placement.
  In V.D. Blondel, E.D. Sontag, M. Vidyasagar, and J.C. Willems, editors, Open Problems in Mathematical Systems and Control Theory, chapter 37, pages 181-191. Springer-Verlag, London, Berlin, New York, 1998.

• J. Rosenthal and F. Sottile. Some remarks on real and complex output feedback.
  Systems & Control Letters, 33(2):73-80, 1998.
  Further details on this paper.

• M. S. Ravi, J. Rosenthal, and X. Wang. Degree of the generalized Plücker embedding of a quot scheme and quantum cohomology.
  Math. Ann., 311(1):11-26, 1998.
  Springer site for downloading the paper.

• W. Helton, J. Rosenthal and X. Wang, Matrix extensions and eigenvalue completions, the generic case.
  Trans. Amer. Math. Soc. 349(8): pp. 3401-3408, 1997.

• J. Rosenthal and X. Wang, Output feedback pole placement with dynamic compensators.
  IEEE Trans. Automat. Contr., 6:830--843, 1996.

• M. S. Ravi, J. Rosenthal, and X. Wang, Dynamic pole assignment and Schubert calculus.
  SIAM J. Control Optim., 34:813-822, 1996.
  (ps.gz file)

• M. S. Ravi, J. Rosenthal, and U. Helmke. Output Feedback Invariants
  Linear Algebra Appl., 351-352:623-637, 2002.
  E-print math.OC/12054, December 2000.
  (PDF file)

• V. G. Lomadze, M. S. Ravi, J. Rosenthal, and J. M. Schumacher. A behavioral approach to singular systems.
  Acta Appl. Math. 54:331--344, 1998.

• M. S. Ravi, J. Rosenthal, and U. Helmke. On output feedback invariants and cascade equivalence of systems.
  In Proc. of the 36th IEEE Conference on Decision and Control, pages 4243-4248, San Diego, California, 1997.
  (ps.gz file)

• M. S. Ravi, J. Rosenthal, and J. M. Schumacher. Homogeneous behaviors. Math. Contr., Sign., and Syst., 10:61-75, 1997.
  CWI Report BS-R9607, June 1996.
  (ps.gz file)

• J. Rosenthal and J. M. Schumacher, Realization by Inspection.
  IEEE Trans. Automat. Control. 42(9): 1257-1263, 1997.
  (ps.gz file)

• D. N. Hoover, R. Longchamp and J. Rosenthal. Two-Degree-of-Freedom $\ell_2$-Optimal Tracking with Preview.
  Automatica, to appear.

• J. Rosenthal and A. Zelevinsky. Multiplicities of points on Schubert varieties in Grassmannians
  Journal of Algebraic Combinatorics, 13:213--218, 2001.
  E-print math.AG/9901057, January 1999.
  (PDF file)

• B. Allen and J. Rosenthal. A matrix Euclidean algorithm induced by state space realization.
  Linear Algebra Appl. 288:105--121, 1999.
  (ps.gz file)
  (PDF file)

• J. Rosenthal, An observability criterion for dynamical systems governed by Riccati differential equations.
  IEEE Trans. Automat. Contr., 41:434--436, 1996.
  

Research supported by NSF Grant No. DMS-96-10389 , DMS-00-72383 , DMS-01-39236 and CCR-ITR--02-05310 .
In the following the homepages of some of my coauthors:
Joan-Josep Climent, Heide Gluesing-Luerssen, Guangyue Han, Gerard Maze, Chris Monico, M. S. Ravi, Hans Schumacher, Roxana Smarandache, Frank Sottile , Alex Wang, Paul Weiner, Jan C. Willems , Pascal Vontobel , Andrei Zelevinsky.

PhD Theses:

• Brian Allen,
  Linear Systems Analysis and Decoding of Convolutional Codes. University of Notre Dame, August 1999.
  PDF file.
  Compressed gzip file.
• Guangyue Han,
  Space Time Coding with Multiple Antenna Systems. University of Notre Dame, May 2004.
  
• Gerard Maze,
  Algebraic Methods for Constructing One-Way Trapdoor Functions. University of Notre Dame, May 2003.
  
• Christopher Monico,
  Semirings and Semigroup Actions in Public-Key Cryptography. University of Notre Dame, May 2002.
  Compressed gzip file.
• Roxana Smarandache,
  Maximum Distance Separable Convolutional Codes, Construction and Decoding. University of Notre Dame, August 2001.
  Compressed gzip file.
• Paul Weiner,
  Multidimensional Convolutional Codes. University of Notre Dame, May 1998.
  Compressed gzip file.
• Eric York,
  Algebraic Description and Construction of Error Correcting Codes, a Systems Theory Point of View. University of Notre Dame, May 1997.
  Compressed gzip file.

Miscellaneous:

"Inverse Eigenvalue Problems for Multivariable Linear Systems",

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