Journal ArticleDOI
On the linear complexity of Legendre sequences
TLDR
The linear complexity of all Legendre sequences and the (monic) feedback polynomial of the shortest linear feedback shift register that generates such a Legendre sequence are determined.Abstract:
We determine the linear complexity of all Legendre sequences and the (monic) feedback polynomial of the shortest linear feedback shift register that generates such a Legendre sequence. The result shows that Legendre sequences are quite good from the linear complexity viewpoint.read more
Citations
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Journal ArticleDOI
Autocorrelation values of generalized cyclotomic sequences of order two
TL;DR: The generalized cyclotomic sequence of order two has several good randomness properties and behaves like the Legendre sequence in several aspects and could have very good autocorrelation property and pattern distributions of length two if the two primes are chosen properly.
Journal ArticleDOI
Permutation polynomials over finite fields from a powerful lemma
Pingzhi Yuan,Cunsheng Ding +1 more
TL;DR: Using a lemma proved by Akbary, Ghioca, and Wang, several theorems on permutation polynomials over finite fields are derived, which give not only a unified treatment of some earlier constructions of permutation Polynomial, but also new specific permutations polynOMials over F q .
Journal ArticleDOI
Linear complexity of new generalized cyclotomic sequences of order two of length pq
TL;DR: In this correspondence, the linear complexity and minimal polynomial of new generalized cyclotomic sequences of order two are determined and it is shown that these sequences also have high linear complexity.
Journal ArticleDOI
Binary sequences with optimal autocorrelation
Ying Cai,Cunsheng Ding +1 more
TL;DR: A well rounded treatment of binary sequences with optimal autocorrelation is given.
Journal ArticleDOI
Linear complexity profile of binary sequences with small correlation measure
Nina Brandstätter,Arne Winterhof +1 more
TL;DR: For a given binary sequence, its linear complexity profile is estimated in terms of the correlation measure, which was introduced by Mauduit and Sárközy, and certain periodic sequences including Legendre sequences, Sidelnikov sequences and other sequences related to the discrete logarithm are applied.
References
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BookDOI
A classical introduction to modern number theory
Kenneth Ireland,Michael Rosen +1 more
TL;DR: This second edition has been corrected and contains two new chapters which provide a complete proof of the Mordell-Weil theorem for elliptic curves over the rational numbers, and an overview of recent progress on the arithmetic of elliptic curve.
Book ChapterDOI
On the Randomness of Legendre and Jacobi Sequences
TL;DR: This paper proposes a new candidate problem, namely the problem of predicting a sequence of consecutive Legendre (Jacobi) symbols modulo a prime (composite), when the starting point and possibly also the prime is unknown.