A new result on the distinctness of primitive sequences over Z/(pq) modulo 2

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• 作者：Qun-Xiong Zheng^a ; ^{qunxiong_zheng@163.com"" rel=""nofollow} ; Wen-Feng Qi^a ; ^b ; ^{wenfeng.qi@263.net"" rel=""nofollow}
• 关键词：Integer residue rings ; Linear recurring sequences ; Primitive polynomials ; Primitive sequences ; Modular reduction
• 刊名：Finite Fields and Their Applications
• 出版年：2011
• 出版时间：May 2011
• 年：2011
• 卷：17
• 期：3
• 页码：254-274
• 全文大小：243 K

文摘

Let Z/(pq) be the integer residue ring modulo pq with odd prime numbers p and q. This paper studies the distinctness problem of modulo 2 reductions of two primitive sequences over Z/(pq), which has been studied by H.J. Chen and W.F. Qi in 2009. First, it is shown that almost every element in Z/(pq) occurs in a primitive sequence of order n>2 over Z/(pq). Then based on this element distribution property of primitive sequences over Z/(pq), previous results are greatly improved and the set of primitive sequences over Z/(pq) that are known to be distinct modulo 2 is further enlarged.