(f(x), m)-interleaved sequences over Fq have been proposed and studied. Roughly speaking, an (f(x), m)-interleaved sequence is a sequence which is made of (or say, interleaved by) m component sequences with a common c...
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(f(x), m)-interleaved sequences over Fq have been proposed and studied. Roughly speaking, an (f(x), m)-interleaved sequence is a sequence which is made of (or say, interleaved by) m component sequences with a common characteristic polynomial (f(x)(∈Fq [x]). in this note, (7(x), m)-interleaved sequences are studied further. As a result, it is made clear how their minimal characteristic polynomials, linear spans and periods are determined by their component sequences. And also, their period distribution and the number of (f(x), m)-interleaved sequences with maximal linear spans are derived. Furthermore, a large number of interleaved sequences with the lowest correlation among ali the (f(x), m)-interleaved sequences are constructed.
The multiplication of points on elliptic curves is the most important operation in the implementation of elliptic curve cryptosystems. Based on Frobenius map, a fast multiplication on the curves defined by y2 + xy = x...
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The multiplication of points on elliptic curves is the most important operation in the implementation of elliptic curve cryptosystems. Based on Frobenius map, a fast multiplication on the curves defined by y2 + xy = x3 + x2 + 1 over finite fields of characteristic 2 is given, and its optimality in the sense of using minimal numbers of additions of points is proved.
In this paper, the theory of continued fractions of algebraic functions will be used to give a general theorem on lower bounds for class numbers of real quadratic function fields K=k(D). The bounds are given more expl...
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In this paper, the theory of continued fractions of algebraic functions will be used to give a general theorem on lower bounds for class numbers of real quadratic function fields K=k(D). The bounds are given more explicitly for six types of real quadratic function fields. As a consequence, six classes of real quadratic function fields with ideal class number greater than one are given.[
LetR be a finite commutative ring with identity and τ be a nonnegative integer. In studying linear finite automata, one of the basic problems is how to characterize the class of rings which have the property that eve...
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LetR be a finite commutative ring with identity and τ be a nonnegative integer. In studying linear finite automata, one of the basic problems is how to characterize the class of rings which have the property that every (weakly) invertible linear finite automaton ? with delay τ over R has a linear finite automaton ?′ over R which is a (weak) inverse with delay τ of ?. The rings and linear finite automata are studied by means of modules and it is proved that *-rings are equivalent to self-injective rings, and the unsolved problem (for τ=0) is solved. Moreover, a further problem of how to characterize the class of rings which have the property that every invertible with delay τ linear finite automaton ? overR has a linear finite automaton ?′ over R which is an inverse with delay τ′ for some τ′?τ is studied and solved.
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