An algorithm for generating shift-register cycles

We consider a certain natural generalization of de Bruijn words, and use it to compute the exact maximum state complexity for the language consisting of the conjugates of a single word. In other words, we determine the state complexity of cyclic shift on languages consisting of a single word.

Generalized de Bruijn Words and the State Complexity of Conjugate Sets

We compute the exact maximum state complexity for the language consisting of m words of length N, and characterize languages achieving the maximum. We also consider a special case, namely languages C ( w ) consisting of the conjugates of a single word w. The words for which the maximum state complexity of C ( w ) is achieved turn out to be a natural generalization of de Bruijn words. We show that generalized de Bruijn words exist for each length and consider the number of them.

Maximal State Complexity and Generalized de Bruijn Words

La mayoria de autores que abordan el tema de la complejidad lineal de secuencias binarias generadas para su aplicacion criptografica se limitan a definir familias muy especificas de filtrados no lineales para los que se puede acotar la complejidad lineal de sus correspondientes secuencias generadas. Aqui se introduce una nueva linea original para el problema de la complejidad lineal para un rango amplio y general de filtrados no lineales. Nuevos conceptos permiten determinar cotas inferiores y superiores al valor de la complejidad lineal

Avances en el estudio de la complejidad lineal del filtrado no lineal

We compute the exact maximum state complexity for the language consisting of $m$ words of length $N$, and characterize languages achieving the maximum. We also consider a special case, namely languages $C(w)$ consisting of the conjugates of a single word $w$. The words for which the maximum state complexity of $C(w)$ is achieved turn out to be a natural generalization of de Bruijn words. We show that generalized de Bruijn words exist for each length and consider the number of them.

Using the Euclidean Algorithm for polynomials over GF(q), an algebraic technique for the generation of q-ary shift register sequences of arbitrary length l, 1 ≤ l ≤ qm, is obtained, where q is a power of a prime number, q = pn, and m is the number of shift register stages.

An Algebraic Construction for q-ary Shift Register Sequences

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An Algebraic Construction for q-ary Shift Register Sequences