Publications of Keith E. Mellinger
Research
articles
(.pdf preprints)
1. A note on line-Baer subspace partitions of PG(3,4), J. Geom. 72 (2001) 128-131.
2. A geometric relationship between equivalent spreads, Designs, Codes and Cryptog. 30: 1 (2003) 63-71.
3. with Norman Johnson, Multiple spread retraction, Adv. Geom. 3: 3 (2003) 263-286.
4. with Jon-Lark Kim & Vera Pless, Projections of binary linear codes onto larger fields, SIAM J. Discrete Math. 16: 4 (2003) 591-603.
5. with Ron Baker, Craig Culbert, & Gary Ebert, Odd order flag-transitive affine planes of dimension three over their kernel, Adv. Geom. – special issue dedicated to Adriano Barlotti. (2003), suppl. S215-S223.
6. Classical mixed partitions, Discrete Math. 283: 1-3 (2004) 267-271.
7. LDPC codes from triangle-free line sets, Designs, Codes and Cryptog.- special issue with proceedings from the 3rd Pythagorean Conf. 32: 1-3 (2004) 341-350.
8. with Norman Johnson, Classification of triply-retractive semifields of order q4, J. Geom. 80 (2004) 121-135.
9. Mixed partitions of PG(3,q2), Finite Fields Appl. 10: 4 (2004) 626-635.
10. with Dhruv Mubayi, Constructions of bipartite graphs from finite geometries, J. Graph Theory. 49: 1 (2005) 1-10.
11. 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.
12. with Jennifer Stovall, A new class of LDPC codes in PG(4,q), ΠME Journal., 12: 5 (2006) 289-295.
13. 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.
14. Classes of codes from quadratic surfaces of PG(3,q), Contributions to Discrete Mathematics, 2: 1 (2007) 35-42.
15. with Tim Alderson, Constructions of optical orthogonal codes from finite geometry, SIAM J. Discrete Math. 21: 3 (2007) 785-793.
16. with Gary Ebert, Mixed partitions and related designs, Designs, Codes and Cryptog. 44: 1-3 (2007) 15-23.
17. 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, pages 51-70.
18. with Tim Alderson, Classes of optical orthogonal codes from arcs in root subspaces, Discrete Math. 308: 7 (2008) 1093-1101.
19. with Tim Alderson, Partitions in finite geometry and related constant composition codes, Innov. Incidence Geom., 8 (2008) 49-71.
20. with Tim Alderson, Families of optimal OOCs with λ = 2, IEEE Trans. Inform. Theory. 54: 8 (August 2008) 3722-3724.
21. with Tim Alderson, Geometric Constructions of Optimal OOCs, Adv. Math. Commun. 2: 4 (2008) 451-467.
22. with Tim Alderson,
2-Dimensional optical orthogonal codes
from Singer groups, Discrete Appl. Math. 157: 14 (2009) 3008-3019.
23. with Catherine Castleberry and Katie Hunsberger, LDPC codes arising from hyperovals, to appear in Bull. Inst. Combin. Appl.
24. with Tim Alderson,
Classes of permutation arrays in finite projective spaces, to appear in Int. J. Inform. Coding Theory.
25. with Jacob Farinholt, Minimal generators for BCH codes, to appear in ΠME Journal.
26. with Felix Lazebnik and Oscar
Vega, On the number of k-gons in finite
projective planes, submitted.
27. with Tim Alderson, Spreads, arcs, and multiple wavelength codes, submitted.
undergraduate student coauthors
Go to Mellinger’s Undergraduate Research Page for more information about my projects with undergraduate students.
Expository
and teaching oriented papers
(.pdf preprints)
1. Designs, geometry, and a golfer's dilemma, Math Mag.,77: 4 (2004) 275-282.
2. Ordering elements and subsets: examples for student understanding, J. Math. Comp. Educ. 38: 3 (2004) 333-337.
3. with Hisaya Tsutsui, Structuring undergraduate research in abstract algebra, Missouri J. Math. Sci., 18: 3 (2006) 206-212.
4. with Felix Lazebnik, Advice for Graduating PhD Students, FOCUS, the newsletter of the MAA, 26: 6 Aug/Sept (2006) 14-15.
5. with Ezra (Bud) Brown, Kirkman's schoolgirls wearing hats and walking through fields of numbers, Math Mag. 82: 1 (2009) 3-15.
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