Linear Complexity for Sequences with Characteristic Polynomial f v Alex
نویسندگان
چکیده
We present several generalisations of the GamesChan algorithm. For a fixed monic irreducible polynomial f we consider the sequences s that have as characteristic polynomial a power of f . We propose an algorithm for computing the linear complexity of s given a full (not necessarily minimal) period of s. We give versions of the algorithm for fields of characteristic 2 and for arbitrary finite characteristic p, the latter generalising an algorithm of Kaida et al. We also propose an algorithm which computes the linear complexity given only a finite portion of s (of length greater than or equal to the linear complexity), generalising an algorithm of Meidl. All our algorithms have linear computational complexity. The algorithms for computing the linear complexity when a full period is known can be further generalised to sequences for which it is known a priori that the irreducible factors of the minimal polynomial belong to a given small set of polynomials.
منابع مشابه
Institutional Repository Linear complexity for sequences with characteristic polynomial fv
We present several generalisations of the GamesChan algorithm. For a fixed monic irreducible polynomial f we consider the sequences s that have as characteristic polynomial a power of f . We propose an algorithm for computing the linear complexity of s given a full (not necessarily minimal) period of s. We give versions of the algorithm for fields of characteristic 2 and for arbitrary finite ch...
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