Source: https://miamioh.edu/cec/academics/departments/cse/about/faculty-and-staff/bibak-khodakhast/index.html
Timestamp: 2019-04-18 20:28:20+00:00

Document:
My paper "Explicit formulas for..." proves a very general result which gives, as consequences, the weight enumerators of several important classes of deletion correcting codes and some of their variants which have been recently used in studying DNA-based data storage systems. Our general results might have more applications/implications in information theory, computer science, and mathematics.
My paper "Unweighted linear congruences with distinct..." studies an arithmetic function and then, as a consequence, gives the weight distribution of the important Varshamov–Tenengolts codes. There are also interesting connections to combinatorics.
My paper "A generalization of Schönemann’s theorem..." generalizes a result of Schönemann from 1839 using a graph theoretic method.
My paper "The Cayley graphs associated with..." using tools from spectral graph theory, character theory, and finite fields, solves a conjecture (stemming from coding theory) appeared in IEEE Trans. Inform. Theory.
My paper "Counting surface-kernel epimorphisms..." gives, as a corollary, an ‘equivalent’ form of the famous and influential Harvey’s theorem on the cyclic groups of automorphisms of compact Riemann surfaces. There are also motivations from string theory and quantum field theory.
My paper "On an almost-universal hash function family..." is the first paper that introduces applications of Ramanujan sums, finite Fourier transform, and restricted linear congruences in the study of universal hashing.
My paper "MMH∗ with arbitrary modulus..." simply generalizes the well-known ∆-universal hash function family, MMH∗.
My paper "Restricted linear congruences" strongly generalizes a result of Rademacher from 1925 and Brauer from 1926 and many others. There are also direct applications to the “generalized knapsack problem" and many other things.
My paper "On fully split..." studies a problem in factorizations of sparse polynomials over finite fields using a rather unusual combination of some techniques including some graph theory arguments.
My paper "Degree-equipartite graphs" solves a problem posed by some leading combinatorialists. This also automatically generalizes the main result of their paper (and another paper published in Trans. Amer. Math. Soc.) too.
1. (K. Bibak, O. Milenkovic) Explicit formulas for the weight enumerators of some classes of deletion correcting codes, submitted.
2. (K. Bibak, B. M. Kapron, V. Srinivasan) A generalization of Schönemann's theorem via a graph theoretic method, submitted.
3. (K. Bibak, O. Milenkovic) Weight enumerators of some classes of deletion correcting codes, In Proceedings of the 2018 IEEE International Symposium on Information Theory --- ISIT 2018, Vail, Colorado, USA, Jun. 17-22, 2018.
4. (K. Bibak, B. M. Kapron, V. Srinivasan) Unweighted linear congruences with distinct coordinates and the Varshamov-Tenengolts codes, Designs, Codes and Cryptography 86 (2018), 1893–1904.
5. (K. Bibak, B. M. Kapron, V. Srinivasan, L. Tóth) On an almost-universal hash function family with applications to authentication and secrecy codes, International Journal of Foundations of Computer Science 29 (2018), 357-375.
6. (K. Bibak, B. M. Kapron, V. Srinivasan, R. Tauraso, L. Tóth) Restricted linear congruences, Journal of Number Theory 171 (2017), 128–144.
7. (K. Bibak, B. M. Kapron, V. Srinivasan) The Cayley graphs associated with some quasi-perfect Lee codes are Ramanujan graphs, IEEE Transactions on Information Theory 62 (2016), 6355–6358.
8. (K. Bibak, B. M. Kapron, V. Srinivasan, L. Tóth) On a variant of multilinear modular hashing with applications to authentication and secrecy codes, In Proceedings of the International Symposium on Information Theory and Its Applications — ISITA 2016, Monterey, California, USA, Oct. 30 – Nov. 2, 2016, pp. 320–324.
9. (K. Bibak, B. M. Kapron, V. Srinivasan) On a restricted linear congruence, International Journal of Number Theory 12 (2016), 2167–2171.
10. (K. Bibak, B. M. Kapron, V. Srinivasan) MMH∗ with arbitrary modulus is always almost-universal, Information Processing Letters 116 (2016), 481–483.
15. (K. Bibak) On the determinant of bipartite graphs, Discrete Mathematics 313 (2013), 2446–2450.
16. (K. Bibak, R. Tauraso) Determinants of grids, tori, cylinders and Mobius ladders, Discrete Mathematics 313 (2013), 1436–1440.
17. (M. H. Shirdareh Haghighi, K. Bibak) The number of spanning trees in some classes of graphs, Rocky Mountain Journal of Mathematics 42 (2012), 1183–1195.
18. (K. Bibak, M. H. Shirdareh Haghighi) Degree-equipartite graphs, Discrete Mathematics 311 (2011), 888–891.
19. (K. Bibak, M. H. Shirdareh Haghighi) Some trigonometric identities involving Fibonacci and Lucas numbers, Journal of Integer Sequences 12 (2009), Article 09.8.4.
20. (M. H. Shirdareh Haghighi, K. Bibak) Recursive relations for the number of spanning trees, Applied Mathematical Sciences 3 (2009), 2263–2269.
21. (M. H. Shirdareh Haghighi, K. Bibak) Distribution of cycle lengths in graphs with minimum degree at least three, In Proceedings of the 39th Annual Iranian Mathematics Conference, Shahid Bahonar University of Kerman, Kerman, Iran, Aug. 24–27, 2008.
22. (K. Bibak, I. E. Shparlinski) On fully split lacunary polynomials in finite fields, Bulletin of the Polish Academy of Sciences, Mathematics 59 (2011), 197–202.
23. (K. Bibak) Problem # 1884, Mathematics Magazine, Vol. 84, No. 5, December 2011.
24. (K. Bibak) Problem # 11590, American Mathematical Monthly, Vol. 118, No. 7, August-September 2011.
25. (K. Bibak) Number theoretic methods and their significance in computer science, information theory, combinatorics, and geometry, PhD thesis, Department of Computer Science, University of Victoria, 2017.
26. (K. Bibak) Contributions at the interface between algebra and graph theory, Master’s thesis, Depart- ment of Combinatorics and Optimization, University of Waterloo, 2013.
27. (K. Bibak, C. Liu, H. Vosoughpour, G. Yao, Z. AlMeraj, A. Pytel, W. Cowan, S. Mann) Implicit surfaces seminar, Spring 2012, Technical Report CS-2013-08, David R. Cheriton School of Computer Science, University of Waterloo, 2013 (40 pages).
International Symposium on Information Theory and Its Applications — ISITA 2016, Monterey, California, USA, Oct. 30 – Nov. 2, 2016.
Conference on Geometry, Algebra, Number Theory, and their Information Technology Applications, The Fields Institute, Toronto, June 13–16, 2016.
2015 Midwest Number Theory Conference, University of Illinois at Chicago, October 16–18, 2015.
International Conference IPM 20 — Combinatorics 2009, IPM, Tehran, Iran, May 15–21, 2009.

References: V. 
 V. 
 V. 
 V. 
 V. 
 V. 
 V. 
 V.