The weight hierarchy of a binary linear [n, k] code C is the sequence (d 1, d 2, . . . , d k ), where d r is the smallest support of an r-dimensional subcode of C. The codes of dimension 4 are collected in classes and...The weight hierarchy of a binary linear [n, k] code C is the sequence (d 1, d 2, . . . , d k ), where d r is the smallest support of an r-dimensional subcode of C. The codes of dimension 4 are collected in classes and the possible weight hierarchies in each class is determined by finite projective geometries. The possible weight hierarchies in class A, B, C, D are determined in Part (I). The possible weight hierarchies in class E, F, G, H, I are determined in Part (II).展开更多
In this paper, we study some results of extended timed event graph (ETEG)by using graph theory's methods in the dioid framework. A necessary and sufficient con-dition for the observability of ETEG is obtained and ...In this paper, we study some results of extended timed event graph (ETEG)by using graph theory's methods in the dioid framework. A necessary and sufficient con-dition for the observability of ETEG is obtained and ETEG's standard structure is alsoestablished.展开更多
This work is devoted to asymptotic properties of a sign-error adaptive filtering algorithm with constant step size. Under much weaker conditions than those that appear in the literature, we obtain convergence and rate...This work is devoted to asymptotic properties of a sign-error adaptive filtering algorithm with constant step size. Under much weaker conditions than those that appear in the literature, we obtain convergence and rate of convergence by using weak convergence methods. An example is provided to demonstrate the performance of the algorithm.展开更多
基金supported by The Norwegian Research Councilthe National Science Foundation of China(10271116)
文摘The weight hierarchy of a binary linear [n, k] code C is the sequence (d 1, d 2, . . . , d k ), where d r is the smallest support of an r-dimensional subcode of C. The codes of dimension 4 are collected in classes and the possible weight hierarchies in each class is determined by finite projective geometries. The possible weight hierarchies in class A, B, C, D are determined in Part (I). The possible weight hierarchies in class E, F, G, H, I are determined in Part (II).
文摘In this paper, we study some results of extended timed event graph (ETEG)by using graph theory's methods in the dioid framework. A necessary and sufficient con-dition for the observability of ETEG is obtained and ETEG's standard structure is alsoestablished.
基金The first author was supported in part by the National Science Foundation of USA(Grant No. DMS-9877090), and the second author was supported in part by the National Key Project of China and the National Natural Science Foundation of China.
文摘This work is devoted to asymptotic properties of a sign-error adaptive filtering algorithm with constant step size. Under much weaker conditions than those that appear in the literature, we obtain convergence and rate of convergence by using weak convergence methods. An example is provided to demonstrate the performance of the algorithm.
