Quadratic forms of codimension 2 over finite fields containing F-4 and Artin-Schreier type curves

Date

2012-03-01

Author

Özbudak, Ferruh
Saygi, Zulfukar

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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).

Subject Keywords

Maximal curve, Quadratic form, Artin-Schreier type curve

URI

https://hdl.handle.net/11511/41850

Journal

FINITE FIELDS AND THEIR APPLICATIONS

DOI

https://doi.org/10.1016/j.ffa.2011.09.008

Collections

Department of Mathematics, Article

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Citation Formats

F. Özbudak and Z. Saygi, “Quadratic forms of codimension 2 over finite fields containing F-4 and Artin-Schreier type curves,” FINITE FIELDS AND THEIR APPLICATIONS, pp. 396–433, 2012, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/41850.