A general construction of inter-group complementary (IGC) codes is proposed based on perfect complementary (PC) codes,interleaving operation,and the orthogonal matrix.The correlation properties of the newly constructe...A general construction of inter-group complementary (IGC) codes is proposed based on perfect complementary (PC) codes,interleaving operation,and the orthogonal matrix.The correlation properties of the newly constructed IGC codes can be described as follows:(1) the autocorrelation sidelobes of the codes are zeros in the zero correlation zone (ZCZ);(2) the cross-correlation functions (CCFs) between any two different codes of the same group are zeros in the ZCZ;(3) the CCFs between any two codes of different groups are zeros everywhere.The key point of this construction is that the ZCZ length of the generated IGC codes can be chosen flexibly.It is well known that there is a limitation between the ZCZ length and the number of mates;that is,the smaller is the length of ZCZ,the more are the IGC codes that can be generated.Therefore,if we can choose the ZCZ length of the IGC codes flexibly according to the requirement of the system,more users can be accommodated in the system.展开更多
Let G be a finite abelian group,M a set of integers and S a subset of G.We say that M and S form a splitting of G if every nonzero element g of G has a unique representation of the form g=m s with m∈M and s∈S,while ...Let G be a finite abelian group,M a set of integers and S a subset of G.We say that M and S form a splitting of G if every nonzero element g of G has a unique representation of the form g=m s with m∈M and s∈S,while 0 has no such representation.The splitting is called purely singular if for each prime divisor p of|G|,there is at least one element of M is divisible by p.In this paper,we continue the study of purely singular splittings of cyclic groups.We prove that if k≥2 is a positive integer such that[−2 k+1,2 k+2]^(∗)splits a cyclic group Z m,then m=4 k+2.We prove also that if M=[−k_(1),k_(2)]^(∗)splits Z m purely singularly,and 15≤k_(1)+k_(2)≤30,then m=1,or m=k_(1)+k_(2)+1,or k_(1)=0 and m=2 k_(2)+1.展开更多
基金Project supported by the National Natural Science Foundation of China (Nos. 61001110,60773074,and 60903004)the China Post-doctoral Science Foundation (No. 20100470204)+1 种基金the Beijing Municipal Natural Science Foundation (No. 4082020)the National High-Tech R & D Program of China (Nos. 2007AA01Z213 and 2009AA01Z209)
文摘A general construction of inter-group complementary (IGC) codes is proposed based on perfect complementary (PC) codes,interleaving operation,and the orthogonal matrix.The correlation properties of the newly constructed IGC codes can be described as follows:(1) the autocorrelation sidelobes of the codes are zeros in the zero correlation zone (ZCZ);(2) the cross-correlation functions (CCFs) between any two different codes of the same group are zeros in the ZCZ;(3) the CCFs between any two codes of different groups are zeros everywhere.The key point of this construction is that the ZCZ length of the generated IGC codes can be chosen flexibly.It is well known that there is a limitation between the ZCZ length and the number of mates;that is,the smaller is the length of ZCZ,the more are the IGC codes that can be generated.Therefore,if we can choose the ZCZ length of the IGC codes flexibly according to the requirement of the system,more users can be accommodated in the system.
文摘Let G be a finite abelian group,M a set of integers and S a subset of G.We say that M and S form a splitting of G if every nonzero element g of G has a unique representation of the form g=m s with m∈M and s∈S,while 0 has no such representation.The splitting is called purely singular if for each prime divisor p of|G|,there is at least one element of M is divisible by p.In this paper,we continue the study of purely singular splittings of cyclic groups.We prove that if k≥2 is a positive integer such that[−2 k+1,2 k+2]^(∗)splits a cyclic group Z m,then m=4 k+2.We prove also that if M=[−k_(1),k_(2)]^(∗)splits Z m purely singularly,and 15≤k_(1)+k_(2)≤30,then m=1,or m=k_(1)+k_(2)+1,or k_(1)=0 and m=2 k_(2)+1.
