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Results on lcz sequences and quadratic forms

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2009
Saygı, Elif
In this thesis we study low correlation zone (LCZ) sequence sets and a class of quadratic forms. In the first part we obtain two new classes of optimal LCZ sequence sets. In our first construction using a suitable orthogonal transformation we extend some results of [21]. We give new classes of LCZ sequence sets defined over Z4 in our second construction. We show that our LCZ sequence sets are optimal with respect to the Tang, Fan and Matsufiji bound [37]. In the second part we consider some special linearized polynomials and corresponding quadratic forms. We compute the number of solutions of certain equations related to these quadratic forms and we apply these result to obtain curves with many rational points.