Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9492926 | Finite Fields and Their Applications | 2005 | 15 Pages |
Abstract
Let p be a prime number, p⩾5, Z/(pe) the integer residue ring, e⩾2, Î={0,1,â¦,pâ1}. For a sequence Ä over Z/(pe), there is a unique decomposition aÌ=aÌ0+aÌ1·p+â¯+aÌeâ1·peâ1, where aÌi be the sequence over Î. Let f(x) be a primitive polynomial with degree n over Z/(pe), Ä and bÌ sequences generated by f(x) over Z/(pe), aÌâ 0(modpeâ1); we prove that the distribution of zeroes in the sequence aÌeâ1=(aeâ1(t))t⩾0 contains all information of the original sequence Ä, that is, if aeâ1(t)=0 if and only if beâ1(t)=0 for all t⩾0, then aÌ=bÌ. As a consequence, we have the following results: (i) two different primitive level sequences are linearly independent over Z/(p); (ii) for all positive integer k, aÌeâ1k=bÌeâ1k if and only if aÌ=bÌ.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Xuan-Yong Zhu, Wen-Feng Qi,