Zobrazeno 1 - 10
of 176
pro vyhledávání: '"Arne Winterhof"'
Autor:
Kai-Uwe Schmidt, Arne Winterhof
Combinatorics and finite fields are of great importance in modern applications such as in the analysis of algorithms, in information and communication theory, and in signal processing and coding theory. This book contains survey articles on topics su
Algebra and number theory have always been counted among the most beautiful and fundamental mathematical areas with deep proofs and elegant results. However, for a long time they were not considered of any substantial importance for real-life applica
This book is based on the invited talks of the'RICAM-Workshop on Finite Fields and Their Applications: Character Sums and Polynomials'held at the Federal Institute for Adult Education (BIfEB) in Strobl, Austria, from September 2-7, 2012. Finite field
Publikováno v:
IEEE Transactions on Information Theory. 68:7538-7544
The (classical) crosscorrelation is an important measure of pseudorandomness of two binary sequences for applications in communications. The arithmetic crosscorrelation is another figure of merit introduced by Goresky and Klapper generalizing Mandelb
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0f1a900c209b3498981dfc6adae5e895
https://doi.org/10.1109/tit.2022.3184176
https://doi.org/10.1109/tit.2022.3184176
Autor:
Arne WINTERHOF
In this survey we summarize properties of pseudorandomness and non-randomness of some number-theoretic sequences and present results on their behaviour under the following measures of pseudorandomness: balance, linear complexity, correlation measure
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a9245538c2eade4db46d597962ca4b1a
http://arxiv.org/abs/2305.11486
http://arxiv.org/abs/2305.11486
Autor:
Huaning Liu, Arne Winterhof
Publikováno v:
Uniform distribution theory. 16:89-108
Let q be a positive integer and 𝒮 = { x 0 , x 1 , ⋯ , x T − 1 } ⊆ ℤ q = { 0 , 1 , … , q − 1 } {\scr S} = \{{x_0},{x_1}, \cdots ,{x_{T - 1}}\}\subseteq {{\rm{\mathbb Z}}_q} = \{0,1, \ldots ,q - 1\} with 0 ≤ x 0 < x 1 < ⋯ < x T − 1
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f1ac53730f0cffd94d592fb8f9fb853f
https://doi.org/10.2478/udt-2021-0009
https://doi.org/10.2478/udt-2021-0009
Autor:
Zibi Xiao, Arne Winterhof
Publikováno v:
IEEE Transactions on Information Theory. 67:5334-5338
Let $1 be the ordered primitive roots modulo ${p}$ . We study the pseudorandomness of the binary sequence $(\text {s}_ {n})$ defined by ${s}_{n}\equiv \text {g}_{n+1}+{g}_{n+2}\bmod 2,\,\, {n}=0,1,\ldots $ In particular, we study the balance, linear
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https://doi.org/10.1109/tit.2021.3088143
https://doi.org/10.1109/tit.2021.3088143
Autor:
Arne Winterhof, Mehdi Makhul
Publikováno v:
Research in Number Theory. 8
Let $$\varvec{F}_q$$ F q be the finite field of q elements, where $$q=p^r$$ q = p r is a power of the prime p, and $$\left( \beta _1, \beta _2, \dots , \beta _r \right) $$ β 1 , β 2 , ⋯ , β r be an ordered basis of $$\varvec{F}_q$$ F q over $$\v
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7bcf344e5a69c478f50ef794897ab8f1
https://doi.org/10.1007/s40993-022-00335-8
https://doi.org/10.1007/s40993-022-00335-8
Autor:
Leyla Işık, Arne Winterhof
Publikováno v:
Applicable Algebra in Engineering, Communication and Computing. 33:587-595
Let $$\gamma$$ be a generator of a cyclic group G of order n. The least index of a self-mapping f of G is the index of the largest subgroup U of G such that $$f(x)x^{-r}$$ is constant on each coset of U for some positive integer r. We determine the i
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e01f8faf8d7673618897e2c2c3cea0be
https://doi.org/10.1007/s00200-020-00475-3
https://doi.org/10.1007/s00200-020-00475-3
Autor:
Arne Winterhof, Hassan Aly
Publikováno v:
IEEE Transactions on Information Theory. 66:1944-1947
It is known that Hall’s sextic residue sequence has some desirable features of pseudorandomness: an ideal two-level autocorrelation and linear complexity of the order of magnitude of its period $p$ . Here we study its correlation measure of order $
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::953531bfca6c5bb26ec3eb52a9a19747
https://doi.org/10.1109/tit.2019.2951591
https://doi.org/10.1109/tit.2019.2951591