Extremal sequences of polynomial complexity

The joint spectral radius of a bounded set of d × d real matrices is defined to be the maximum possible exponential growth rate of products of matrices drawn from that set. For a fixed set of matrices, a sequence of matrices drawn from that set is called extremal if the associated sequence of partial products achieves this maximal rate of growth. An influential conjecture of J. Lagarias and Y. ...

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Extremal sequences of polynomial complexity 3

The joint spectral radius of a bounded set of d × d real matrices is defined to be the maximum possible exponential growth rate of products of matrices drawn from that set. For a fixed set of matrices, a sequence of matrices drawn from that set is called extremal if the associated sequence of partial products achieves this maximal rate of growth. An influential conjecture of J. Lagarias and Y. ...

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Linear complexity of binary sequences derived from polynomial quotients

We determine the linear complexity of p-periodic binary threshold sequences derived from polynomial quotient, which is defined by the function (u−u)/p (mod p). When w = (p−1)/2 and 2p−1 6≡ 1 (mod p), we show that the linear complexity is equal to one of the following values { p − 1, p − p, (p + p)/2 + 1, (p − p)/2 } , depending whether p ≡ 1, −1, 3, −3 (mod 8). But it seems that the method can’...

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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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Linear Complexity for Sequences with Characteristic Polynomial f v Alex

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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Extremal sequences of polynomial complexity

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