How to determine linear complexity and kk-error linear complexity in some classes of linear recurring sequences

Several fast algorithms for the determination of the linear complexity of $d$-periodic sequences over a finite field \F_q, i.e. sequences with characteristic polynomial $f(x) = x^d-1$, have been proposed in the literature. In this contribution fast algorithms for determining the linear complexity of binary sequences with characteristic polynomial $f(x) = (x-1)^d$ for an arbitrary positive integer $d$, and $f(x) = (x^2+x+1)^{2^v}$ are presented. The result is then utilized to establish a fast algorithm for determining the $k$-error linear complexity of binary sequences with characteristic polynomial $(x^2+x+1)^{2^v}$

Narrative inquiry into (re)imagining alternative schools: a case study of Kevin Gonzales.

Although there are many alternative schools that strive for the successful education for their students, negative images of alternative schools persist. While some alternative schools are viewed as “idealistic havens,” many are viewed as “dumping grounds,” or “juvenile detention centers.” Employing narrative inquiry, this article interrogates how a student, Kevin Gonzales, experiences his alternative education and raises questions about the role of alternative schools. Kevin Gonzales’s story is presented in a literary form of biographical journal to provide a “metaphoric loft” that helps us imagine other students like Kevin. This, in turn, provokes us to examine our current educational practice, and to (re)imagine ways in which alternative education can provide the best possible educational experiences for disenfranchised students who are increasingly underserved by the public education system