Correlation of sequences and quadratic forms

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2017
Genişel, Cansu
Sequences are widely used in code division multiple access communication systems. In a shared communication channel distinct sequences are assigned to distinct users. Low correlation sequences should be used in order to separate each user. In this thesis, quadratic forms and their properties are introduced. Sequence families constructed by quadratic forms and their correlations are studied. We give a construction of a binary sequence family when n = 3k and k is an odd integer. This sequence family has six- valued correlation distribution and its maximum correlation magnitude is given. Our sequence family is a subfamily of Generalized Modified Gold sequence family. At the end, we compare the correlation properties of our sequence family with some other known sequence families.