无限长序列的周期与广度的关系

The relationship of period and width of infinite sequences

码字广度的研究对于刻画码字的复杂性以及码字的分类具有重要意义.定义了有限域GF(pm)和环Zpm上(p是大于2的素数,m≥1)上无限长序列的广度,证明了如果序列x=(x0,x1,…)的广度有限width(x)=w>0,则x的最小周期为2p「logpw」;反之,当x的最小周期为2pi+1时,若广度w有限,则w满足pi<w≤pi+1(从而pi+1=p「logpw」).

It is important to study widths of codewords and characterize complexity of codewords.In this paper the width of an infinite sequence over finite fields GF（pm） and rings Zpm is defined,where p is an odd prime and m≥1.It is shown that the least period of a sequence x=（x0,x1,…）is 2pif the width of x=（x0,x1,…） is finite number width（x）=w0.Conversely,if the least period of a sequence x=（x0,x1,…）is 2pi＋1and the width of x=（x0,x1,…） is w,then w satisfies piw≤pi＋1 and therefore pi＋1=p「logpw」.