Asymptotic Behavior of Normalized Linear Complexity of Multi-sequences
Asymptotic Behavior of Normalized Linear Complexity of Multi-sequences
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DOI：
10.1007/11423461_7
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发表时间：
2004-10
期刊：
影响因子：
--
通讯作者：
Z. Dai;K. Imamura;Junhui Yang
中科院分区：
文献类型：
--
作者：
Z. Dai;K. Imamura;Junhui Yang
Asymptotic behavior of the normalized linear complexity $\frac{L_{\b{s}}(n)}{n}$ of a multi-sequence s̱ is studied in terms of its multidimensional continued fraction expansion, where $L_{\b{s}}(n)$ is the linear complexity of the lengthnprefix of s̱ and defined to be the length of the shortest multi-tuple linear feedback shift register which generates the lengthnprefix of s̱. A formula for $\lim \sup _{n\rightarrow\infty}\frac{L_{\b{s}}(n)}{n}$ together with a lower bound, and a formula for $\lim \inf_{n\rightarrow\infty}\frac{L_{\b{s}}(n)}{n}$ together with an upper bound are given. A necessary and sufficient condition for the existence of $\lim_{n\rightarrow\infty}\frac{L_{\b{s}}(n)}{n}$ is also given.
Asymptotic behavior of the normalized linear complexity $\frac{L_{\b{s}}(n)}{n}$ of a multi-sequence s̱ is studied in terms of its multidimensional continued fraction expansion, where $L_{\b{s}}(n)$ is the linear complexity of the lengthnprefix of s̱ and defined to be the length of the shortest multi-tuple linear feedback shift register which generates the lengthnprefix of s̱. A formula for $\lim \sup _{n\rightarrow\infty}\frac{L_{\b{s}}(n)}{n}$ together with a lower bound, and a formula for $\lim \inf_{n\rightarrow\infty}\frac{L_{\b{s}}(n)}{n}$ together with an upper bound are given. A necessary and sufficient condition for the existence of $\lim_{n\rightarrow\infty}\frac{L_{\b{s}}(n)}{n}$ is also given.