Two families of Niho sequences having four-valued cross correlation with m-sequences Dedicated to Professor Yingbo Zhang on the Occasion of His 70th Birthday  

作　　者：FAN JinMei XU YunGe XIA YongBo ZENG XiangYong 

机构地区：[1]Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathematics,Hubei University [2]College of Science, Guilin University of Technology [3]Department of Mathematics and Statistics, South-Central University for Nationalities

出　　处：《Science China Mathematics》2017年第12期2377-2390,共14页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No. 61170257)

摘　　要：For two odd integers m and s with 1≤s < m and gcd(m, s) = 1, let h satisfy h(2~s-1) ≡1(mod 2~m+ 1) and d =(h + 1)(2~m-1) + 1. The cross correlation function between a binary m-sequence of period 22~m-1 and its d-decimation sequence is proved to take four values, and the correlation distribution is completely determined. Let n be an even integer and k be an integer with 1≤k≤n/2. For an odd prime p and a p-ary m-sequence {s(t)} of period p^n-1, define u(t) =∑(p^k-1)/2 i=0 s(d_it), where d_i = ip^(n/2) + p^k-i and i = 0, 1,...,(p^k-1)/2. It is proved that the cross correlation function between {u(t)} and {s(t)} is three-valued or four-valued depending on whether k is equal to n/2 or not, and the distribution is also determined.For two odd integers m and s with 1≤s 〈 m and gcd（m, s） = 1, let h satisfy h（2~s-1） ≡1（mod 2~m＋ 1） and d =（h ＋ 1）（2~m-1） ＋ 1. The cross correlation function between a binary m-sequence of period 22~m-1 and its d-decimation sequence is proved to take four values, and the correlation distribution is completely determined. Let n be an even integer and k be an integer with 1≤k≤n/2. For an odd prime p and a p-ary m-sequence {s（t）} of period p^n-1, define u（t） =∑（p^k-1）/2 i=0 s（d_it）, where d_i = ip^（n/2） ＋ p^k-i and i = 0, 1,...,（p^k-1）/2. It is proved that the cross correlation function between {u（t）} and {s（t）} is three-valued or four-valued depending on whether k is equal to n/2 or not, and the distribution is also determined.

关 键 词：M-SEQUENCE decimation sequence correlation distribution Niho exponent exponential sum 

分 类 号：O156[理学—数学]