次最优跳频序列集的构造

A NEW CONSTRUCTION OF SUBOPTIMAL FREQUENCY HOPPING SEQUENCE SETS

分圆类和分圆数是数论和组合数学中的经典议题.它们与差集,序列设计,以及编码理论存在着密切的关联.而寻求和设计比较理想(最优及次最优)的跳频序列(集)则是研究跳频通信技术的重要课题.文章基于广义分圆类提出一种次最优跳频序列集的构造,这些序列集具有新的参数且序列长度能为任意大于3的奇数.

Cyclotomy and cyclotomic numbers are classic topics of number theory and combinatorics.They are closely related to difference sets,sequences and coding theory.To find optimal and suboptimal frequency hopping sequence sets is an important subject in the research of frequency hopping multiple-access systems.In this paper,based on a generalized cyclotomy,we propose a new construction of suboptimal frequency hopping sequence sets with respect to the Peng-Fan bound.Those frequency hopping sequence sets have parameters（v,f,e ＋ l;（v-1）/e）,where v —p_1^（m1）p_2^（m2）…p_k^（mk） is an odd integer larger than 3,p_i is prime for 1 ≤ i ≤ k,e｜（p_i-1） for 1 ≤ i ≤ k and f = min {^（p_1-1）/e：1≤i≤ k}.Some of the frequency hopping sequence sets proposed in this paper can have new parameters compared with the known frequency hopping sequence sets in the literature.