| Summary: | 碩士 === 國立中山大學 === 通訊工程研究所 === 104 === A sequence is defined as perfect if and only if the out-of-phase value of the periodic autocorrelation function (PACF) is equal to zero. Furthermore, the degree of a sequence is defined as distinct nonzero elements within one period of the sequence. This paper proposes method based on cyclotomic field and finite field theory for systematically constructing perfect sequences with composite length which can be factored into N=2p, where p is an odd prime. The study start by partitioning a set ZN={1,2,...,N-1} into three exclusive subset C0,C1,C2, where one of subset C0 whose elements are coprime with N and the reminder subset are based on the subset C0 to construct. Due to the subset C0 have property of multiplication group and cyclic group, and subset C1 is established by the subset C0, we can partition cyclic group C0,C1, into K coset of M cardinality , where p-1=KM. According to this partition, the four-degree and (2K+2)-degree perfect sequences are constructed by using two different approaches, where these approach are designed to satisfy the time-domain ideal PACF property and the frequency-domain flat magnitude spectrum requirement, respectively.
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