Heeralal Janwa

Address College of Natural Sciences
Department of Mathematics
17 University Ave. Ste 1701
San Juan, PR 00925-2537
Office NCN II C-120
Office Hours
Program
Telephone (787) 764-0000 88266
E-Mail moc.liamg@awnajh ude.rpu@awnaj.lalareeh
MathSciNet Link

Education

PhD, Syracuse University, 1986

Research

Coding Theory; Cryptography; Applied Algebra; Algebraic Geometry over Finite Fields and Computations.

Selected Publications

  1. H. Janwa and H. F. Mattson, Jr., “The covering radii of even subcodes of t-dense codes,” Springer-Verlag Lecture Notes in Computer Science, vol. 229, pp. 120-130, 1986. (Invited.)
  2. H. Janwa and H.F. Mattson, Jr., “The covering radii and normality of t-dense codes,” Proceeding of the IEEE International Symposium on Information Theory (ISIT), Ann Arbor, Michigan, October 6-9, 1986.
  3. H. Janwa, “Some new upper bounds on the covering radii of binary linear codes,” IEEE Transactions on Information Theory, vol. IT-35, no. 1, pp. 110–122, January 1989.
  4. H. Janwa, “Some optimal codes from algebraic geometry and their covering radii,” European Journal of Combinatorics, vol. 11, pp. 249–266, 1990.
  5. H. Janwa, “On the covering radii of q-ary codes.” Proceedings of the IEEE International Symposium on Information Theory (ISIT), January 14–19, 1990, San Diego, California.
  6. R. Dougherty and H. Janwa, “Covering radius computations for binary cyclic codes,”, Mathematics of Computation, Vol. 57, no. 195, July 1991, pp. 415–434.
  7. R. Doubherty and H. Janwa, “Appendix–Results of Covering Radius Computations,” Mathematics of Computation, Vol. 57, no. 195, July 1991, s38—-s218. (As Microfiche supplements.)
  8. H.T. Cao, R. Dougherty and H. Janwa, “A [55,16,19] Binary Goppa Code and Related Codes Having Large Minimum Distance,” IEEE Transactions on Information Theory, Vol. 37, no. 5, September 1991, pp. 1432–1433.
  9. H. Janwa, “On the parameters of algebraic-geometric codes,” Proceedings of the 9th International Conference on Algebraic Algorithms and Error-Correcting Codes (AAECC), New Orleans, USA, October 7-10, 1991. Springer-Verlag Lecture Notes in Computer Science (LNCS), No. 593, October 1991, pp. 19–28. (Invited). (Refereed by three referees.)
  10. H. Janwa, THE MAN WHO KNEW INFINITY: A Life of the Genius Ramanujan, in The Political and Economical Weekly of India, September 26, 1992, pp. 2105–2106.
  11. H. Janwa and R.M. Wilson, “Hyperplane section*s of Fermat varieties in IP 3 in char. 2 and some applications to cyclic codes,” Proceedings of the 10th International Conference on AAECC, LNCS, No. 673, 1993, pp. 180–194. (Refereed by three referees.)
  12. H. Janwa, THE MAN WHO KNEW INFINITY: A Life of the Genius Ramanujan, By Robert Kanigel; Bombay Mathematical Colloquium, March 1993;
  13. H. Janwa and O. Moreno, “McEliece-Public Key Cryptosystems Using Algebraic Geometric Codes,” Proceedings of the 1995 IEEE International Symposium on Information Theory (ISIT), British Columbia, Sept. 17–22, 1995, p. 484-484. The conference had 19 long papers among 600 total.
  14. H. Janwa, G. McGuire, and R.M. Wilson, “Double-error-correcting cyclic codes and absolutely irreducible polynomials over GF(2),” Journal of Algebra, vol. 178, pp. 665–676, 1995.
  15. H. Janwa and O. Moreno, “Elementary Constructions of Some Ramanujan Graphs,” Congressus Numer- antium, vol. 112, pages 7-15, December 1995.
  16. H. Janwa, “Public Key Cryptosystems Using Algebraic Geometric Codes,” Proceedings of the National Discussion Meeting on Cryptography and Computation, held at JNCASR, IISc. Bangalore, India, September, 1995.
  17. H. Janwa and O. Moreno, “McEliece like public-key cryptosystems using algebraic-geometric codes,” Designs, Codes and Cryptography, vol. 8, no. 3, pp. 293–307, 1996.
  18. H. Janwa and A.K. Lal, “On the generalized Hamming weights of cyclic codes,” IEEE Transactions on Information Theory, Vol. 43, No. 1, pp. 298–308, January 1997.
  19. H. Janwa and O. Moreno, “Strongly Ramanujan graphs from codes, polyphase-sequences, and Combina- torics,” Proceedings of the International Symposium on Information Theory, 1997 (ISIT-97) Ulm, Germany., 1997, pp. 408-408, The Conference had 18 long papers among total about 600.
  20. H. Janwa and O. Moreno, “Coding theoretic constructions of some number theoretic Ramanujan graphs,” Congressus Numerantium, Vol. 130, pp. 63–76, 1998.
  21. H. Janwa and H.F. Mattson, Jr., “Some Upper Bounds on the Covering Radii of Linear Codes over Fq and Their Applications,” Designs, Codes and Cryptography, Vol. 18, no. 1-3, December 1999, pp. 163–181. (invited.)
  22. H. Janwa, Jr., “Relations among Expander Graphs, Codes, Sequence Design, and Their Applications,” in Proceedings of the 4th World Multi-conference on Systemics, Cybernetics and Informatics (SCI2000) and ISAS2000), Orlando Florida, July 23-26, 2000, Vol. XI, pp. 122-124.(invited—Organized by Jacque Wolfmann)
  23. H. Janwa and H.F. Mattson, Jr., “The Projective Hypercube and Its Properties and Applications," Pro- ceedings of the 2001 International Symposium on Information Theory, (ISIT-2001) June 2001, Washington, USA., p. 312-312. (3 1/2 regular size printed pages.)
  24. H. Janwa and A.K. Lal, ““A Comparison of Minimum Distance Bounds on Tanner Codes,” Proceedings of the 39th Allerton Conference on Communication, Control, and Computing, pp. 1294–1296, December 2001.
  25. H. Janwa and A.K.Lal, “On Tanner Codes: Parameters and Decoding,” Applicable Algebra in Engineering, Communication and Computing, A Springer Journal, Vol. 13, pp. 335–347, 2003.
  26. H. Janwa, “Good Expander Graphs and Expander Codes: Parameters and Decoding,” Proceedings of the 15th International Symposium on Algebraic Algorithms and Error-Correcting Codes (AAECC-15), Toulouse, France, May 2003. Springer-Verlag Lecture Notes in Computer Science (LNCS), No. 2643, May, 2003, pp. 119–128. (Refereed)
  27. H. Janwa (With A.K. Lal). "On Expander Graphs: Parameters and Applications” arXiv:cs.IT/0406048:2004, pp. 1—11..
  28. H. Janwa, “New (Explicit) Constructions of Asymptotic Families of Constant Degree Expander Graphs from AG Codes and Their Applications to Tanner Codes,” ABSTRACTS OF THE AMS, Volume 26, no. 1, pp. 197. (JOINT AMS ANNUAL MEETING, Atlanta, USA, 2005; (Invitation only) Special session on Algebraic Geometry and Codes.)) (Invited Talk)
  29. H. Janwa, “Explicit Constructions of Asymptotic Families of Constant Degree Expander Graphs from Algebraic Geometric (AG) Codes,” CONGRESSUS NUMERANTIUM, vol. 179, 2006, pp. 193–207.
  30. H. Janwa and A.K. Lal,“On the Generalized Hamming Weights and the Covering Radius of Linear Codes," Lecture Notes in Computer Science, Vol. 4871, pp. 347—356, December 2007.
  31. H. Janwa, “Ramanujan graphs and Optimal Expander Graphs from Algebraic Geometric Codes,” H. Janwa, ”Expanders and Ramanujan Graphs: Construction and Applications.” ABSTRACTS of the AMS, Volume 29, No. 1, P. 223. (JOINT AMS ANNUAL MEETING, San Diego, CA, USA, 2008; (Invitation Only) Special session on Expander Graphs and Ramanujan Graphs.)) (one hour invited talk).
  32. H. Janwa, Tom Hoeholdt, “Optimal Bipartite Ramanujan Graphs from Balanced Incomplete Block Designs: Their Characterizations and Applications to Expander/ LDPC Codes” Lecture Notes in Computer Science, Vol. 5527, pp. 53—64, June 2009.
  33. H. Janwa, F. Pinero, “On the Parameters of Norm Trace codes,” CONGRESSUS NUMERANTIUM, Vol. 206 (2010), PP. 99-113.
  34. H. Janwa, F. Pinero, “On the Subfield Subcodes of Hermitian Codes,” it Proceedings of the 3rd International Castle Meeting on Coding Theory and Applications, J. Borges and M. Villanueva (eds.), pp. 223—229, 2011
  35. H. Janwa (with Tom Hoeholdt), "Eigenvalues and expansion of bipartite graphs" Designs, Codes and Cryptography ( invited article in Honor of Prof. R. M. Wilson’s 65th birthday), December 2012, Volume 65, Issue 3, pp 259-273.
  36. H.Janwa(withM.Delgado),“OntheConjectureonAPNFunction,"arXiv:1207.5528[cs.IT][math.AG][math.CO 23 July 2012, pp. 1—15.
  37. H. Janwa, “Some Applications of Groebner Bases to Combinatorics,” in Combinatorial Topology and Algebra. Lecture Notes in Mathematics, Ramanujan Mathematical Society, Journal. Vol. 18, pages 1994–205, 2013.
  38. H. Janwa (with M. Delgado), “Further Results on Exceptional APN Functions,” www.math.iitb.ac.in/ srg/AGCT India-2013/Slides/HeeralalJanwa.pdf.
  39. H. Janwa (with F. Pinero), “On the subfield subcodes of Hermitian codes,” Designs, Codes and Cryptography,, Designs, Codes and Cryptography, January 2014, Volume 70, issue 1-2m pp. 157-173.
  40. H. Janwa (with P. Vijay Kumar and Andrew Z. Tirkel), “In Memoriam: Oscar Moreno de Ayala (1946–2015), IEEE Information Theory Society News Letter, December 2015, pp. 43–44.
  41. H. Janwa (with F. Castro, G. Mullen, and I. Rubio), “On perfect like codes,” Bulletin of the Institute of Combinatorial Mathematics and its Applications, Vol 76, pp. 1—7, January 2016.
  42. H. Janwa (with M. Delgado), “Progress Towards the Conjecture on APN Functions and Absolutely Irreducible Polynomials,” arXiv:1602.02576 [math.NT] 30 Jan. 2016
  43. H. Janwa (with F. Pinero) “On Parameters of Subfield Subcodes of Extended Norm-Trace Codes,” arXiv:1604.05777 [math.AG] , 20 Apr 2016.
  44. H. Janwa (with M. Delgado), “On the absolute irreducibility of hyperplane sections of generalized Fermat varieties in P3 and the conjecture on exceptional APN functions: the Kasami-Welch degree case,” arXiv:1612.05997 [math.AG] 18 Dec.2016
  45. H. Janwa(withM.Delgado),“On the Conjecture on Non-linear APN Functions and Absolutely Irreducibility of Polynomials," Designs, Codes and Cryptography, Springer-Verlag, 82, no. 3, (2017) 627–627. DOI: 10.1007/s10623-015-0168-1
  46. H. Janwa (with M. Delgado), “Some New Results on the Conjecture on Exceptional APN Functions and Absolutely Irreducible Polynomials: the Gold Case,” Advances in Mathematics of Communications (AMC), vol. 11, nov. 2, (2017), pp. 389–396.
  47. H. Janwa (with F. Pinero), “On the Parameters of Subfield Subcodes of Norm Trace Codes,” Advances in Mathematics of Communications (AMC), vol. 11, no. 2, (2017), pp. 379–388.
  48. H. Janwa (with M. Delgado) “On the Completion of the Exceptional APN Conjecture in the Gold Degree Case and Absolutely Irreducible Polynomials,” Congressos Numerantium, October 2017 (accepted)
  49. H. Janwa (with F. Pinero), BCH-like Codes from Extended Norm-Trace Codes, Congressos Numerantium, October 2017 (accepted)
  50. H. Janwa and R. M. Wilson, “Rational Points on the Klein Quartic and the Binary Cyclic Codes ⟨m1m7⟩,” IEEE Transactions on Information Theory (Accepted for publication subject to revision). (12 printed pages.)

Selected Grants and Awards

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