Abstract
Let \({\mathbb F}_q\) be a finite field of characteristic 2, not containing \({\mathbb F}_4\). Let k ≥ 2 be an even integer. We give a full classification of quadratic forms over \({\mathbb F}_{q^k}\) of codimension 2 provided that certain three coefficients are from \({\mathbb F}_4\). We apply this to the classification of maximal and minimal curves over finite fields.
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Acknowledgements
We would like to thank the anonymous reviewers for their detailed and useful comments.
The first and the third authors were partially supported by TÜBİTAK under Grant No. TBAG–109T672. The work of Z. Saygı was also supported by TÜBİTAK under Grant No. TBAG–109T344.
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Özbudak, F., Saygı, E. & Saygı, Z. Quadratic forms of codimension 2 over certain finite fields of even characteristic. Cryptogr. Commun. 3, 241–257 (2011). https://doi.org/10.1007/s12095-011-0051-5
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DOI: https://doi.org/10.1007/s12095-011-0051-5