Existence problem of almost p-ary perfect and nearly perfect sequences

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Tezin Türü: Doktora

Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Türkiye

Tezin Onay Tarihi: 2012

Öğrenci: CEMAL CENGİZ YILDIRIM

Eş Danışman: OĞUZ YAYLA

Danışman: FERRUH ÖZBUDAK

Özet:

Almost p-ary perfect and nearly perfect sequences are equivalent to certain relative difference sets and direct product difference sets, respectively. This feature enables Chee, Tan and Zhou to determine the existence status of those sequences by using the tools of Design Theory. In particular, they determined the existence status of almost p-ary perfect and nearly perfect sequences of period n+1 for n 100, except some open cases in [6]. In this thesis, we obtained a set of Diophantine equations in integers while observing relative difference sets, and proved nonexistence of almost p-ary perfect sequences of period n + 1 for n (50,76,94,99,100).Also, we observed that it was possible to extend Diophantine equations that we used for relative difference sets to the direct product difference sets, thereby proved the nonexistence of almost p-ary nearly perfect sequences of type II of period n + 1 for p = 2, p = 3 and p = 5 at certain values of n. As a result, we answered two questions posed by Chee, Tan and Zhou in [6].