Publications

Research articles

  1. with Jeremy Dover and Kenneth Wantz, A minimum blocking semioval in PG(2,9), J. Geom. 107: 1 (April 2016) 119-123.
  2. with Oscar Vega and Ryan Vaughn*, Graphs embedded into finite projective planes, Contrib. Discrete Math. 10: 1 (2015).
  3. with Jeremy Dover, Small Kakeya sets in non-prime order planes,  European J. Combin.  47 (2015), 95–102.
  4. with Jeremy Dover, Some spectral results on Kakeya sets, Adv. Geom.,  15: 3 (July 2015) 333-338.
  5. with Jeremy Dover and Kelly Scott*, Minimal Kakeya sets, J. Comb. Designs, 22: 2 (February 2014) 95-104.
  6. with Felix Lazebnik and Oscar Vega, Embedding cycles in finite planes, Elec. J. Combinatorics, 20: 3 (2013) P24.
  7. with Jeremy Dover and Kenneth Wantz, Blocking semiovals containing conics, Adv. Geom. 13: 1 (January 2013) 29-40.
  8. with Jeremy Dover and Kenneth Wantz, Generalized Pellegrino caps, Finite Fields Appl. 18: 5 (September 2012) 946–955.
  9. with Noga Alon, Dhruv Mubayi and Jacques Verstraete, The de Bruijn-Erdös theorem for hypergraphs, Designs, Codes and Cryptog. 65: 3 (2012) 233-245.
  10. with Jeremy Dover, Semiovals from unions of conics, Innov. Incidence Geom., 12 (2011) 61-83.
  11. with Tim Alderson, Spreads, arcs, and multiple wavelength codes, Discrete Math., 311: 13 (6 July 2011) 1187-1196.
  12. with Jacob Farinholt,* Minimal generators for BCH codes, ΠME Journal., 13: 4 (Spring 2011) 199-206.
  13. with Tim Alderson, Classes of permutation arrays in finite projective spaces, Int. J. Inform. Coding Theory. 1: 4 (2010) 371-383.
  14. with Catherine Castleberry* and Katie Hunsberger*, LDPC codes arising from hyperovals, Bull. Inst. Combin. Appl.58 (2010) 59-72.
  15. with Felix Lazebnik and Oscar Vega, On the number of k-gons in finite projective planes, Note Mat., vol 29 suppl. 1 (2009) 135-152.
  16. with Tim Alderson, 2-Dimensional optical orthogonal codes from Singer groups, Discrete Appl. Math. 157: 14 (2009) 3008-3019.
  17. with Tim Alderson, Geometric constructions of optimal OOCs, Adv. Math. Commun. 2: 4 (2008) 451-467.
  18. with Tim Alderson, Families of optimal OOCs with λ = 2, IEEE Trans. Inform. Theory. 54: 8 (August 2008) 3722-3724.
  19. with Tim Alderson, Partitions in finite geometry and related constant composition codes, Innov. Incidence Geom., 8 (2008) 49-71.
  20. with Tim Alderson, Classes of optical orthogonal codes from arcs in root subspaces, Discrete Math. 308: 7 (2008) 1093-1101.
  21. with Tim Alderson, Optical orthogonal codes from Singer groups, in the book Advances in Coding Theory and Cryptology, edited by T. Shaska, W. C. Huffman, D. Joyner, V. Ustimenko, Series on Coding Theory and Cryptology, 2. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ (2007) 51-70.
  22. with Jon-Lark Kim and Leo Storme, Small weight codewords in LDPC codes defined by (dual) classical generalized quadrangles, Designs, Codes and Cryptog, 42: 1 (2007) 73-92.
  23. with Gary Ebert, Mixed partitions and related designs, Designs, Codes and Cryptog. 44: 1-3 (2007) 15-23.
  24. with Tim Alderson, Constructions of optical orthogonal codes from finite geometry, SIAM J. Discrete Math. 21: 3 (2007) 785-793.
  25. Classes of codes from quadratic surfaces of PG(3,q), Contrib. Discrete Math, 2: 1 (2007) 35-42.
  26. with Jennifer Stovall*, A new class of LDPC codes in PG(4,q), ΠME Journal., 12: 5 (2006) 289-295.
  27. with Sean Droms* and Chris Meyer*, LDPC codes generated by conics in the classical projective plane, Designs, Codes and Cryptog. 40: 3 (2006) 343-356.
  28. with Dhruv Mubayi, Constructions of bipartite graphs from finite geometries, J. Graph Theory. 49: 1 (2005) 1-10.
  29. Mixed partitions of PG(3,q2), Finite Fields Appl.10: 4 (2004) 626-635.
  30. with Norman Johnson, Classification of triply-retractive semifields of order q4, J. Geom.80 (2004) 121-135.
  31. LDPC codes from triangle-free line sets, Designs, Codes and Cryptog. 32: 1-3 (2004) 341-350.
  32. Classical mixed partitions, Discrete Math. 283: 1-3 (2004) 267-271.
  33. with Ron Baker, Craig Culbert, & Gary Ebert, Odd order flag-transitive affine planes of dimension three over their kernel, Adv. Geom. (2003), suppl. S215-S223.
  34. with Jon-Lark Kim & Vera Pless, Projections of binary linear codes onto larger fields, SIAM J. Discrete Math. 16: 4 (2003) 591-603.
  35. with Norman Johnson, Multiple spread retraction, Adv. Geom. 3: 3 (2003) 263-286.
  36. A geometric relationship between equivalent spreads, Designs, Codes and Cryptog. 30: 1 (2003) 63-71.
  37. A note on line-Baer subspace partitions of PG(3,4), J. Geom. 72 (2001) 128-131.

* – undergraduate student coauthors

Expository and teaching oriented papers

  1. with Raymond Viglione, Completing the proof of a geometry classic, submitted.
  2. with Raymond Viglione, The Spider and the Fly, College Math J. 43: 2 (2012) 169-173.
  3. with Ezra (Bud) Brown, Kirkman’s schoolgirls wearing hats and walking through fields of numbers, Math Mag. 82: 1 (2009) 3-15. MAA Carl B. Allendoerfer Award, 2010.
  4. with Felix Lazebnik, Advice for Graduating PhD Students, FOCUS, the newsletter of the MAA, 26: 6 Aug/Sept (2006) 14-15.
  5. with Hisaya Tsutsui, Structuring undergraduate research in abstract algebra, Missouri J. Math. Sci., 18: 3 (2006) 206-212.
  6. Ordering elements and subsets: examples for student understanding, J. Math. Comp. Educ. 38: 3 (2004) 333-337.
  7. Designs, geometry, and a golfer’s dilemma, Math Mag.,77: 4 (2004) 275-282.

Ph.D. Dissertation

  • Mixed Partitions and Spreads of Projective Spaces
  • Preamble and Chapter 1: Introduction
  • Chapters 2 & 3: The Hirschfeld-Thas Construction; The Classical Examples
  • Chapters 4 & 5: Automorphism Groups; Equivalent Spreads
  • Chapter 6: Examples of Mixed Partitions and Their Associated Translation Planes
  • Chapter 7 to the end: Conclusion; Appendix; Bibliography