Quadratic forms of codimension 2 over certain finite fields of even characteristic

Date

2011-12-01

Author

Özbudak, Ferruh
Saygi, Zulfukar

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Let F-q be a finite field of characteristic 2, not containing F-4. Let k >= 2 be an even integer. We give a full classification of quadratic forms over F-q(k) of codimension 2 provided that certain three coefficients are from F-4. We apply this to the classification of maximal and minimal curves over finite fields.

Subject Keywords

Artin-Schreier type curve, Quadratic form, Maximal curve

URI

https://hdl.handle.net/11511/48047

Journal

CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES

DOI

https://doi.org/10.1007/s12095-011-0051-5

Collections

Department of Mathematics, Article

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Quadratic forms of codimension 2 over finite fields containing F-4 and Artin-Schreier type curves Özbudak, Ferruh; Saygi, Zulfukar (2012-03-01) Let F-q be a finite field containing F-4. Let k >= 2 be an integer. We give a full classification of quadratic forms over F-q(k) of codimension 2 provided that certain three coefficients are from F-4. As an application of this we obtain new results on the classification of maximal and minimal curves over F-q(k) . We also give some nonexistence results on certain systems of equations over F-q(k).
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Subfields of the function field of the deligne-Lusztig curve of ree type Çakçak, Emrah; Akyıldız, Ersan; Özbudak, Ferruh; Department of Mathematics (2002) Let X be the Deligne-Luzstig curve of Ree type defined over ¥q,q = 32s+1, s > 1 and F its function field. One of the main problem here is to construct a large number of nonrational subfields of F and compute their genera. For this, we consider the fixed fields FH, of F, under subgroups H of G, where G = Aut(F/F9) is the automor phism group of F/Fg. In this thesis, we show how one can compute the genera of FH for various subgroups H of G. Our computation here is based on the facts that: G is a Ree group whic...

Citation Formats

F. Özbudak and Z. Saygi, “Quadratic forms of codimension 2 over certain finite fields of even characteristic,” CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES, pp. 241–257, 2011, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/48047.