Constructions of pseudorandom binary lattices using cyclotomic classes in finite fields
In 2006, Hubert, Mauduit and Sárközy extended the notion of binary sequences to n-dimensional binary lattices and introduced the measures of pseudorandomness of binary lattices. In 2011, Gyarmati, Mauduit and Sárközy extended the notions of family complexity, collision and avalanche effect from bina...
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Online Access: | https://doi.org/10.1515/math-2020-0086 |
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doaj-6c22381838304b1d93e4e6371ed982732021-09-06T19:20:12ZengDe GruyterOpen Mathematics2391-54552020-12-011811606161410.1515/math-2020-0086math-2020-0086Constructions of pseudorandom binary lattices using cyclotomic classes in finite fieldsChen Xiaolin0School of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, Shanxi, People’s Republic of ChinaIn 2006, Hubert, Mauduit and Sárközy extended the notion of binary sequences to n-dimensional binary lattices and introduced the measures of pseudorandomness of binary lattices. In 2011, Gyarmati, Mauduit and Sárközy extended the notions of family complexity, collision and avalanche effect from binary sequences to binary lattices. In this paper, we construct pseudorandom binary lattices by using cyclotomic classes in finite fields and study the pseudorandom measure of order k, family complexity, collision and avalanche effect. Results indicate that such binary lattices are “good,” and their families possess a nice structure in terms of family complexity, collision and avalanche effect.https://doi.org/10.1515/math-2020-0086pseudorandombinary latticecyclotomic classfinite fieldcharacter sum11k4511b5094a5594a60 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Chen Xiaolin |
spellingShingle |
Chen Xiaolin Constructions of pseudorandom binary lattices using cyclotomic classes in finite fields Open Mathematics pseudorandom binary lattice cyclotomic class finite field character sum 11k45 11b50 94a55 94a60 |
author_facet |
Chen Xiaolin |
author_sort |
Chen Xiaolin |
title |
Constructions of pseudorandom binary lattices using cyclotomic classes in finite fields |
title_short |
Constructions of pseudorandom binary lattices using cyclotomic classes in finite fields |
title_full |
Constructions of pseudorandom binary lattices using cyclotomic classes in finite fields |
title_fullStr |
Constructions of pseudorandom binary lattices using cyclotomic classes in finite fields |
title_full_unstemmed |
Constructions of pseudorandom binary lattices using cyclotomic classes in finite fields |
title_sort |
constructions of pseudorandom binary lattices using cyclotomic classes in finite fields |
publisher |
De Gruyter |
series |
Open Mathematics |
issn |
2391-5455 |
publishDate |
2020-12-01 |
description |
In 2006, Hubert, Mauduit and Sárközy extended the notion of binary sequences to n-dimensional binary lattices and introduced the measures of pseudorandomness of binary lattices. In 2011, Gyarmati, Mauduit and Sárközy extended the notions of family complexity, collision and avalanche effect from binary sequences to binary lattices. In this paper, we construct pseudorandom binary lattices by using cyclotomic classes in finite fields and study the pseudorandom measure of order k, family complexity, collision and avalanche effect. Results indicate that such binary lattices are “good,” and their families possess a nice structure in terms of family complexity, collision and avalanche effect. |
topic |
pseudorandom binary lattice cyclotomic class finite field character sum 11k45 11b50 94a55 94a60 |
url |
https://doi.org/10.1515/math-2020-0086 |
work_keys_str_mv |
AT chenxiaolin constructionsofpseudorandombinarylatticesusingcyclotomicclassesinfinitefields |
_version_ |
1717777072857808896 |