Constructions Of Quaternary (Odd) Periodic Complementary Pairs

Two sequences are called a periodic(resp.,an odd periodic)complementary pair if the sum of their periodic(resp.,odd periodic)autocorrelation functions is a delta function.(odd)periodic complementary pair sequences have been widely used in modern communications,cryptography,radar detection,sonar and other fields.In addition,(odd)periodic complementary pairs are closely related to difference sets.In this thesis,we focus on the constructions of quaternary periodic(odd periodic)complementary pairsFirstly,three general methods for constructing quaternary periodic complementary pairs are given.The first method is based on inverse mapping of Gray mapping and binary odd periodic complementary pairs,and constructs quaternary periodic complementary pairs with odd length.The second method constructs quaternary periodic complementary pairs with even length by making modified Gray mapping to odd length quaternary periodic complementary pairs.The third method is to construct quaternary periodic complementary pairs of odd length and perfect quaternary sequences of even length by periodic product,and construct quaternary periodic complementary pairs of even length.Compared with known results,the proposed constructions can generate quaternary periodic complementary pairs with new parameters.Based on the constructed quaternary periodic complementary pairs,quaternary Hadamard matrices are also obtained.Secondly,two general methods for constructing quaternary odd periodic complementary pairs are given.The first method is based on inverse mapping of Gray mapping and binary odd periodic complementary pairs,and constructs quaternary odd periodic complementary pairs with odd length.Next,odd period complementary pairs of odd length and even length odd perfect quaternary sequences are multiplied by odd period products to construct odd-period complementary pairs of even length.Both methods can generate quaternary odd periodic complementary pairs with new parameters.Based on the constructed quaternary odd periodic complementary pairs,quaternary Hadamard matrices are constructed.In addition,by using a special class of quaternary odd periodic complementary pairs,a nearly optimal binary periodic almost complementary pair is constructed.