P. VIJAY KUMAR

JOURNAL PAPERS - Under Review

  1. A. Chang, T. Helleseth and P. V. Kumar, "A new triple-error correcting code and relation to a conjectured ideal autocorrelation sequence," submitted to IEEE Trans. Inform. Theory, Dec, 1998.

  2. K. Yang, Y. Kim, and P. V. Kumar, "Quasi-Orthogonal Sequences for Code-Division Multiple Access Systems," submitted to the IEEE Trans. Information Theory, November 1998.

  3. A. Chang, P. Gaal, S. W. Golomb, G. Gong and P. V. Kumar, "Some results relating to a sequence conjectured to have ideal autocorrelation," submitted to IEEE Trans. Inform. Theory, Summer, 1998.

  4. D. Shin, P. V. Kumar and T. Helleseth, "3-designs from the Z_4-Goethals code via a new Kloosterman sum identity," submitted to Designs, Codes and Cryptography, Fall 1998.

  5. D. Shin, P. V. Kumar and T. Helleseth, "An Assmus-Mattson-type approach for identifying t-designs from linear codes over Z4," submitted to to Designs, Codes and Cryptography, Fall 1998.

  6. D. Shin, P. V. Kumar and T. Helleseth, "5-designs from the lifted Golay code over Z4 via ann Assmus-type approach," submitted to Discrete Mathematics, Fall 1998.

JOURNAL PAPERS [Published/(to Appear)]

  1. T. Helleseth, P.V. Kumar, and K. Yang, "An infinite family of 3-designs from Preparata codes over Z_4," Designs, Codes and Cryptography, vol. 15, pp. 175-181, 1998.

  2. A.G. Shanbhag, P.V. Kumar, and T. Helleseth, "An upper bound for extended Kloosterman sums over Galois rings," Finite Fields and Their Applications, vol. 4, pp. 218-238, 1998.

  3. P.V. Kumar and T. Helleseth, "An Expansion for the coordinates of the trace function in Galois rings," Applicable Algebra in Engineering, Communication and Computing, Vol. 8, No. 5, pp. 353-362, 1997.

  4. T. Helleseth, P. Vijay Kumar and A. G. Shanbhag, "Codes with the same weight distribution as the Goethals codes and the Delsarte-Goethals codes," Designs, Codes and Cryptography, vol. 9, pp. 257-266, November, 1996.

  5. K. Yang, T. Helleseth, P. V. Kumar and A. Shanbhag, "The weight hierarchy of Kerdock codes over Z_4," IEEE Transactions on Information Theory, vol. IT-42, pp. 1587-1593, September, 1996.

  6. A. Shanbhag, P. V. Kumar and T. Helleseth, "Improved Binary Codes and Sequence Families from Z_4-Linear Codes, IEEE Transactions on Information Theory, vol. IT-42, pp. 1582-1586, September, 1996.

  7. T. Helleseth, P. V. Kumar, O. Moreno and A. G. Shanbhag, "Improved estimates via exponential sums for the minimum distance of Z_4-linear trace codes," IEEE Transactions on Information Theory, vol. IT-42, pp. 1212-1216, July, 1996.

  8. T. Helleseth and P. V. Kumar, "On the Weight Hierarchy of the Semiprimitive Codes," Discrete Mathematics, vol. 152, pp. 185-190, May, 1996.

  9. P. V. Kumar, T. Helleseth and A. R. Calderbank, "Large Families of Quaternary Sequences with Low Correlation," IEEE Trans. Inform. Theory, vol. IT-42, pp. 579-592, March, 1996.

  10. A. R. Calderbank, G. McGuire, P. V. Kumar, T. Helleseth, "Cyclic Codes over Z_4, Locator Polynomials, and Newton identities," IEEE Trans. on Inform. Theory, vol. IT-42, pp. 217-226, Jan. 1996.

  11. A. Shanbhag, P. Vijay Kumar and T. Helleseth, "Upper bound for a hybrid sum over Galois rings with applications to aperiodic correlation of some q-ary sequences," IEEE Trans. Inform. Theory, vol. IT-42, pp. 250-254, Jan. 1996.

  12. T. Helleseth and P. V. Kumar, "Algebraic Decoding of the Goethals codes," IEEE Trans. Inform. Theory, vol. IT-41, pp. 2040-2048, Nov. 1995.

  13. T. Helleseth and P. V. Kumar, "The Weight Hierarchy of the Kasami Codes," Discrete Mathematics, vol. 145, (1-3), pp. 133-143, October 1995.

  14. O. Moreno, V. A. Zinoviev and P. V. Kumar, "An Extension of the Weil-Carlitz-Uchiyama Bound," Finite Fields and their Applns vol. 1, no. 3, pp. 306-371, July, 1995.

  15. P. V. Kumar, T. Helleseth and A. R. Calderbank, "An Upper Bound for Weil Exponential Sums over Galois Rings and Applications," IEEE Trans. on Inform. Theory, vol. IT-41, pp. 456-468, March 1995.

  16. O. Moreno, Z. Zhang, V. Zinoviev and P. V. Kumar, "Asymptotically Optimum Families of Optical Orthogonal Codes," IEEE Trans. on Inform. Theory, vol. 41, pp. 448-455, March 1995.

  17. K. C. Yang, P. V. Kumar and H. Stichtenoth "On the Weight Hierarchy of Geometric Goppa Codes", IEEE Trans. on Inform. Theory, vol. IT-40, pp. 913-920, May 1994.

  18. S. Boztas and P. V. Kumar "Binary Sequences with Gold-like Correlation but Larger Linear Span", IEEE Trans. on Inform. Theory, vol. IT-40, pp. 532-537, March 1994.

  19. A. R. Hammons, Jr., P. Vijay Kumar, A. R. Calderbank, N. J. A. Sloane and P. Sole, "The Z_4-Linearity of Kerdock, Preparata, Goethals and Related Codes," IEEE Trans. on Inform. Theory, vol. IT-40, pp. 301-319, March 1994.

  20. O. Moreno and P. V. Kumar, "Minimum Distance Bounds for Cyclic Codes and Deligne's Theorem", IEEE Trans. on Inform. Theory, vol. IT-39, pp. 1524-1534, September 1993.

  21. A. R. Calderbank, A. R. Hammons, Jr., P. V. Kumar, N. J. A. Sloane and P. Sole, "A Linear Construction for Certain Kerdock and Preparata Codes," Bull. Amer. Math. Society, Vol. 29, Number 2, pp. 218-222, October 1993.

  22. A. R. Hammons, Jr., P. V. Kumar "On a Recent Four-Phase Sequence Design," (Invited Paper), Special Issue on Spread-Spectrum Techniques and Applications of the IEICE Trans. on Communications, vol. E 76-B, No. 8, pp. 804-813, August 1993.

  23. P. V. Kumar and V. Wei, "Minimum Distance of Logarithmic and Fractional Partial m-Sequences", IEEE Trans. on Inform. Theory, vol. IT-38, 5, pp.1474-1482, September 1992.

  24. Ara Patapoutian and P. V. Kumar, "The (d,k)-Subcode of a Linear Block Code," IEEE Trans. on Inform. Theory, vol. IT-38, 4, pp. 1375-1382, July 1992.

  25. S. Boztas, R. Hammons, and P.V. Kumar, "4-Phase Sequences with Near-Optimum Correlation Properties", IEEE Trans. on Inform. Theory, vol. IT-38, 3, pp. 1101-1113, May 1992.

  26. P.V. Kumar and O. Moreno, "Prime-Phase Sequences with Periodic Correlation Properties Better than Binary Sequences", IEEE Trans. on Inform. Theory, vol. IT-37, pp. 603-616, May 1991.

  27. H. Chung and P.V. Kumar, "Optical Orthogonal Codes - New Bounds and an Optimal Construction," IEEE Trans. on Inform. Theory, vol. IT-36, pp. 866-873, July 1990.

  28. P.V. Kumar and C. M. Liu, "Lower Bounds to the Maximum Correlation of Complex, Roots-of-Unity Sequences," IEEE Trans. on Inform. Theory, vol. IT-36, No.3, pp.633-640, May 1990.

  29. H. Chung and P. V. Kumar, "A New General Construction for Bent Functions", IEEE Trans. on Inform. Theory, vol. IT-35, pp. 206-210, January 1989.

  30. J.S. No and P.V. Kumar, "A New Family of Pseudorandom Sequences Having Optimal Periodic Correlation Properties and Large Linear Span," IEEE Trans. on Inform. Theory, vol. It-35, pp. 371-379, March 1989.

  31. P.V. Kumar, "On the Existence of Square Dot-Matrix Patterns Having a Specific 3-Valued Periodic-Correlation Function," IEEE Trans. on Inform. Theory, vol. IT-34, no. 2, pp. 271-278, May 1988.

  32. P.V. Kumar, "Frequency-Hopping Code Sequences Having Large Linear Span," IEEE Trans. on Inform. Theory, vol. IT-34, no. 1, pp. 146-151, January 1988.

  33. P.V. Kumar, R.A. Scholtz and L.R. Welch, "Generalized Bent Functions and Their Properties," Journal of Combinatorics, Series A, vol. 40, pp. 90-107, September 1985.

  34. P.V. Kumar and R.A. Scholtz, "Generalized GMW Sequences and an Application to Frequency Hopping," Cryptologic Quarterly, vol. 3, nos. 1-2, pp. 1-5, Spring-Summer, 1984.

  35. P.V. Kumar and R.A. Scholtz, "Bounds on the Linear Span of Bent Sequences," IEEE Trans. on Inform. Theory, vol. IT-29, no. 6, pp. 854-862, November 1983.

REFEREED CONFERENCE PROCEEDINGS

  1. T. Helleseth, P.V. Kumar, K. Yang and C. Rong, "On infinite families of 3-designs from Preparata codes and related codes over Z_4," invited paper presented at the Thirty Fifth Annual Allerton Conference on Communication, Control and Computing, Urbana, IL, Sept. 29-Oct. 1, 1997.

  2. P.V. Kumar and T. Helleseth, "An Expansion for the coordinates of the trace function in Galois rings," invited paper presented at the IEEE Information Theory Workshop, Longyearbyen, Norway, July 6-12, 1997.

  3. T. Helleseth, P.V. Kumar, A.G. Shanbhag, and K. Yang, "On the weight hierarchy of some codes over Z_4," invited paper presented at the IEEE Information Theory Workshop, Longyearbyen, Norway, July 6-12, 1997.

  4. P.V. Kumar and T. Helleseth, "Coordinates of trace sequences in Galois rings," invited paper presented at the Arithmetic, Geometry and coding Theory (AGCT-6) Conference, C.I.R.M., Luminy, Marseilles, France, June 23-27, 1997.

  5. T. Helleseth, P.V. Kumar, A.G. Shanbhag, and K. Yang, "On the weight hierarchy of some codes over Z_4," invited paper presented at the Arithmetic, Geometry, and Coding Theory (AGCT-6) Conference, C.I.R.M, Luminy, Marseille, France, June 23-27, 1997.

  6. P.V. Kumar, "An overview of algebraic geometry codes," invited paper presented at the 12th annual conference of the Ramanujan Mathematical Society, Shimoga, India, May 22-24, 1997.

  7. T. Helleseth, P. V. Kumar and A. Shanbhag, "Exponential sums over Galois rings and their applications," 3rd International Conference on Finite Fields and their Applications, Glasgow, U.K., July 11-14, 1995.

  8. A. R. Hammons, Jr., P. Vijay Kumar, A. R. Calderbank, N. J. A. Sloane and P. Sole, "On the Apparent Duality of the Kerdock and Preparata Codes", (Invited Paper), vol. 673, Lecture Notes in Computer Science, Springer-Verlag, pp.13-24, proceedings of the 10th International Symposium on Applicable Algebra, Error-Correcting Codes, Combinatorics and Computer Algebra, Puerto Rico, May 10-14, 1993.

  9. K. Yang and P. Vijay Kumar, " On the True Minimum Distance of Hermitian Codes", Lecture Notes in Mathematics, Vol. 1518, Springer-Verlag, pp. 99-107, proceedings of the International Workshop on Coding Theory and Algebraic Geometry, Luminy, France, June 17-21, 1991.

INVITED TALKS

  1. "PN Sequences in Galois Rings," Kun-kuk University, Seoul, Korea, April 30, 1997.

  2. "Survey of recent trends algebraic geometric codes," Hanyang University, April 28, 1997.

  3. "Lectures on Algebraic Geometric Codes," a series of roughly a dozen lectures given in Spring 1997 at the Department of Computer Science and Automation in the Indian Institute of Science, Bangalore, India.

BOOKS AND BOOK CHAPTERS

  1. T. Helleseth and P. V. Kumar, "Sequences with Low Correlation", (Invited Book Chapter) in the Handbook of Coding Theory, edited by V. Pless and C. Huffman, Elsevier Science Publishers, 1998.

  2. T. Helleseth and P. V. Kumar, "Pseudonoise Sequences," Mobile Communications Handbook, edited by Jerry D. Gibson (CRC and IEEE Press), 1996.

  3. T. Helleseth and P. V. Kumar, "Pseudonoise Sequences," Communications Handbook, edited by Jerry D. Gibson (CRC and IEEE Press), 1997.

  4. P. V. Kumar "Error-Correcting Codes," (Invited Book Chapter) in Space Communication and Nuclear Scintillation, Edited by Nirode Mohanty, van Nostrand Rheinhold, 1990.
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