Measures of pseudorandomness of families of binary lattices, II (A further construction)

Katalin Gyarmati, Christian Mauduit, A. Sárközy

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

In Part I of this paper we extended the notions of family complexity, collision and avalanche effect from one dimension to n dimensions, i.e., from binary sequences to binary lattices. Then we considered a large family of binary lattices with strong pseudorandom properties which had been constructed by using quadratic characters of finite fields, and we showed that this family also possesses a nice structure in terms of these notions. In Part I we considered a large family of binary sequences with strong pseudorandom properties constructed by using additive characters and we extended it to n dimensions, i.e., to binary lattices. In this paper we will show that these binary lattices possess strong pseudorandom properties, and their family also possesses a nice structure in terms of family complexity, collision and avalanche effect.

Original languageEnglish
Pages (from-to)479-502
Number of pages24
JournalPublicationes Mathematicae
Volume80
Issue number3-4
DOIs
Publication statusPublished - 2012

Fingerprint

Pseudorandomness
Binary
Binary Sequences
Avalanche
Collision
One Dimension
Family
Galois field

Keywords

  • Binary lattice
  • Collision and ava- lanche effect
  • Family complexity
  • Pseudorandom

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Measures of pseudorandomness of families of binary lattices, II (A further construction). / Gyarmati, Katalin; Mauduit, Christian; Sárközy, A.

In: Publicationes Mathematicae, Vol. 80, No. 3-4, 2012, p. 479-502.

Research output: Contribution to journalArticle

@article{7b595a6e141e484aa47a3b5b495e71b4,
title = "Measures of pseudorandomness of families of binary lattices, II (A further construction)",
abstract = "In Part I of this paper we extended the notions of family complexity, collision and avalanche effect from one dimension to n dimensions, i.e., from binary sequences to binary lattices. Then we considered a large family of binary lattices with strong pseudorandom properties which had been constructed by using quadratic characters of finite fields, and we showed that this family also possesses a nice structure in terms of these notions. In Part I we considered a large family of binary sequences with strong pseudorandom properties constructed by using additive characters and we extended it to n dimensions, i.e., to binary lattices. In this paper we will show that these binary lattices possess strong pseudorandom properties, and their family also possesses a nice structure in terms of family complexity, collision and avalanche effect.",
keywords = "Binary lattice, Collision and ava- lanche effect, Family complexity, Pseudorandom",
author = "Katalin Gyarmati and Christian Mauduit and A. S{\'a}rk{\"o}zy",
year = "2012",
doi = "10.5486/PMD.2012.5197",
language = "English",
volume = "80",
pages = "479--502",
journal = "Publicationes Mathematicae",
issn = "0033-3883",
publisher = "Kossuth Lajos Tudomanyegyetem",
number = "3-4",

}

TY - JOUR

T1 - Measures of pseudorandomness of families of binary lattices, II (A further construction)

AU - Gyarmati, Katalin

AU - Mauduit, Christian

AU - Sárközy, A.

PY - 2012

Y1 - 2012

N2 - In Part I of this paper we extended the notions of family complexity, collision and avalanche effect from one dimension to n dimensions, i.e., from binary sequences to binary lattices. Then we considered a large family of binary lattices with strong pseudorandom properties which had been constructed by using quadratic characters of finite fields, and we showed that this family also possesses a nice structure in terms of these notions. In Part I we considered a large family of binary sequences with strong pseudorandom properties constructed by using additive characters and we extended it to n dimensions, i.e., to binary lattices. In this paper we will show that these binary lattices possess strong pseudorandom properties, and their family also possesses a nice structure in terms of family complexity, collision and avalanche effect.

AB - In Part I of this paper we extended the notions of family complexity, collision and avalanche effect from one dimension to n dimensions, i.e., from binary sequences to binary lattices. Then we considered a large family of binary lattices with strong pseudorandom properties which had been constructed by using quadratic characters of finite fields, and we showed that this family also possesses a nice structure in terms of these notions. In Part I we considered a large family of binary sequences with strong pseudorandom properties constructed by using additive characters and we extended it to n dimensions, i.e., to binary lattices. In this paper we will show that these binary lattices possess strong pseudorandom properties, and their family also possesses a nice structure in terms of family complexity, collision and avalanche effect.

KW - Binary lattice

KW - Collision and ava- lanche effect

KW - Family complexity

KW - Pseudorandom

UR - http://www.scopus.com/inward/record.url?scp=84867512647&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867512647&partnerID=8YFLogxK

U2 - 10.5486/PMD.2012.5197

DO - 10.5486/PMD.2012.5197

M3 - Article

AN - SCOPUS:84867512647

VL - 80

SP - 479

EP - 502

JO - Publicationes Mathematicae

JF - Publicationes Mathematicae

SN - 0033-3883

IS - 3-4

ER -