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Further results on rational points of the curve y(qn) - y = gamma xqh+1 - alpha over F-qm
Let q be a positive power of a prime number. For arbitrary positive integers h, n, m with n dividing m and arbitrary gamma, alpha is an element of F-qm with gamma not equal 0 the number of F-qm - rational points of the ...
Explicit maximal and minimal curves over finite fields of odd characteristics
(Academic Press Inc Elsevier Science, 2016-11)
In this work we present explicit classes of maximal and minimal Artin-Schreier type curves over finite fields having odd characteristics. Our results include the proof of Conjecture 5.9 given in  as a very special ...
On the Number of Quadratic Forms Having Codimension 2 Radicals in Characteristic 2 Giving Maximal/Minimal Curves
(Taylor and Francis Inc., 2014-09)
Let F-q be an arbitrary finite field of characteristic 2 and k be an arbitrary even integer. We count the number of quadratic forms having codimension 2 radicals on F-q(k) over F-q such that the corresponding curve is ...
L-Polynomials of the Curve
(Springer Verlag, 2015)
Let chi be a smooth, geometrically irreducible and projective curve over a finite field F-q of odd characteristic. The L-polynomial L-chi(t) of chi determines the number of rational points of chi not only over F-q but also ...
On the exact number of solutions of certain linearized equations
In this note we have revisited some of the results of Trachtenberg (On the cross-correlation functions of maximal linear sequences, Ph.D. thesis, University of Southern California, Los Angeles, 1970), which are directly ...