多重采样序列的极小多项式  

Minimum Polynomial of Multiple Sampling Sequence

作　　者：张春起[1] 杨义先[1] 游林[2] 

机构地区：[1]北京邮电大学信息工程学院,北京100876 [2]大连理工大学应用数学系,大连116023

出　　处：《北京邮电大学学报》2001年第4期11-15,共5页Journal of Beijing University of Posts and Telecommunications

基　　金：国家重点基础研究发展规划项目 (G19990 35 80 5 G19980 30 4 2 0 );国家杰出青年基金项目 (6 94 2 5 0 0 1);国家自然科学基金资助项目 (6 9882 0 0 2 ;6 0 0 730 4 9)

摘　　要：在一定条件下 ,多重采样序列与初态无关 ;多重采样序列以 g(x N1)为生成多项式 ,且存在极小多项式满足 mc(x) =g(x N1)的多重采样序列 ;当控制序列中“1”的个数是 2的幂时 ,多重采样序列的极小多项式为 gt(x) ,周期为 2 r(2 n- 1) ;特殊地 ,当控制序列为 m-序列且 (m,n) =1,m≤ n/2时 ,多重采样序列的极小多项式为 mc(x) =gt(x) ,2 m-2 <t≤ 2 m-1,周期为 2 m-1(2 n - 1)We present mosaic theorem for binary sequence and multiple sampling sequence. Main conclusion includes: multiple sampling sequence has nothing to do with its original state, and g(x N 1 ) is one of its generator polynomial, and there is a SSCO that its minimum polynomial m c (x)=g(x N 1 ); When the number of '1' is power of 2 in the controlled sequence, the minimum polynomial of multiple sampling sequence is g t(x) , its period is 2 r(2 n-1) ; Specially, When the controlled sequence is m Sequence and (m,n)=1,m≤n/2 , the minimum polynomial of multiple sampling sequence is m c (x)=g t(x), its period is 2 m-1 (2 n-1),2 m-2 <t≤2 m-1 .

关 键 词：极小多项式 拼接定理 多重采样序列 周期序列 

分 类 号：O15[理学—数学]