Almost Perfct Binary And Ternary Arrays Pairs Theory

The perfect discrete signal have abroad been applied in modern communic- ation, radar, sonar, navigation, space ranging and controlling, and electronic antagonism systems. Well-structured signals can enhance system's properties of anti-interference, anti-doubts, the decline of performance such as resistance to the system, and increase data confidentiality. Therefore, the study of the perfect discrete signals is of vital importance both in theory and applications.Basing on the international current status of the perfect discrete signal, the almost perfect correlation arrays pairs is selected as the researching matter. The construction is the emphasis in this paper. Firstly, a new block design(divisible difference set pairs)is presented in this paper. Some characters and the necessary and sufficient conditions of existence of the divisible difference set pairs are proved. The relationship between the difference set,divisible difference set,difference set pairs and divisible difference set pairs are researched. By using computer, some examples of the divisible difference set pairs are searched. Secondly, according to the almost perfect binary arrays pairs, the characters and the necessary conditions of existence are presented. The relationship between the almost perfect binary arrays pairs and characteristic polynomial is construct- ed. Array transform, direct, folded transform, period product and recursive construction are proved as the constructions of the almost perfect binary arrays pairs. Lastly, the definition of the almost perfect ternary arrays pairs is presented as the extension of almost perfect binary arrays pairs, it's characters and the necessary conditions were discussed. The relationship between the almost perfect ternary arrays pairs and characteristic polynomial is constructed. At the same time, folded transform, period product and recursive construction is suitable for the almost perfect ternary arrays pairs.The constructions of the almost perfect binary arrays pairs and the almost perfect ternary arrays pairs provide broader choice range of the address yard.