Commutative presemifields and semifields

Advances in Mathematics

Volumn 217, Issue 1, 2008, Pages 282-304

  Coulter, Robert S ^a   Henderson, Marie ^b  

^a UNIVERSITY OF DELAWARE   (United States)

^b NONE   (New Zealand)

Author keywords

Commutative semifield; Dembowski Ostrom polynomial; Planar function

Indexed keywords

EID: 35548975245     PISSN: 00018708     EISSN: 10902082     Source Type: Journal    
DOI: 10.1016/j.aim.2007.07.007     Document Type: Article

References (23)

1. Albert A.A. On nonassociative division algebras. Trans. Amer. Math. Soc. 72 (1952) 296-309
2. Albert A.A. Finite division algebras and finite planes. Combinatorial Analysis: Proceedings of the 10th Symposium in Applied Mathematics. Providence. Symposia in Appl. Math. vol. 10 (1960), American Mathematical Society 53-70
3. Albert A.A. Generalized twisted fields. Pacific J. Math. 11 (1961) 1-8
4. Bosma W., Cannon J., and Playoust C. The Magma algebra system I: The user language. J. Symbolic Comput. 24 (1997) 235-265
5. Cohen S.D., and Ganley M.J. Commutative semifields, two-dimensional over their middle nuclei. J. Algebra 75 (1982) 373-385
6. Coulter R.S. The classification of planar monomials over fields of prime square order. Proc. Amer. Math. Soc. 134 (2006) 3373-3378
7. Coulter R.S., and Matthews R.W. Planar functions and planes of Lenz-Barlotti class II. Des. Codes Cryptogr. 10 (1997) 167-184
8. 2. Math. Z. 103 (1968) 239-258
9. Dickson L.E. On commutative linear algebras in which division is always uniquely possible. Trans. Amer. Math. Soc. 7 (1906) 514-522
10. Ding C., and Yuan J. A family of skew Hadamard difference sets. J. Combin. Theory. Ser. A 113 (2006) 1526-1535
11. Ganley M.J. Central weak nucleus semifields. European J. Combin. 2 (1981) 339-347
12. Gluck D. A note on permutation polynomials and finite geometries. Discrete Math. 80 (1990) 97-100
13. Hiramine Y. A conjecture on affine planes of prime order. J. Combin. Theory Ser. A 52 (1989) 44-50
14. Hiramine Y. On planar functions. J. Algebra 133 (1990) 103-110
15. Kantor W.M. Commutative semifields and symplectic spreads. J. Algebra 270 (2003) 96-114
16. Knuth D.E. Finite semifields and projective planes. J. Algebra 2 (1965) 182-217
17. Lidl R., Mullen G.L., and Turnwald G. Dickson Polynomials. Pitman Monogr. Surv. Pure Appl. Math. vol. 65 (1993), Longman Scientific and Technical, Essex, England
18. Menichetti G. On a Kaplansky conjecture concerning three-dimensional division algebras over a finite field. J. Algebra 47 (1977) 400-410
19. Moore E.H. A doubly-infinite system of simple groups. Bull. New York Math. Soc. 3 (1893) 69-82
20. Moore E.H. A doubly-infinite system of simple groups. Math. Papers read at the Congress of Mathematics. Chicago, 1893 (1896) 208-242
21. Penttila T., and Williams B. Ovoids of parabolic spaces. Geom. Dedicata 82 (2000) 1-19
22. Rónyai L., and Szo{combining double acute accent}nyi T. Planar functions over finite fields. Combinatorica 9 (1989) 315-320
23. Wedderburn J.H.M. A theorem on finite algebras. Trans. Amer. Math. Soc. 6 (1905) 349-352