### Abstract

The linear complexity is an important and frequently used measure of unpredictably and pseudorandomness of binary sequences. In Part I of this paper, we extended this notion to two dimensions: we defined and studied the linear complexity of binary and bit lattices. In this paper, first we will estimate the linear complexity of a truly random bit (M,N)-lattice. Next we will extend the notion of k-error linear complexity to bit lattices. Finally, we will present another alternative definition of linear complexity of bit lattices.

Original language | English |
---|---|

Pages (from-to) | 237-263 |

Number of pages | 27 |

Journal | Ramanujan Journal |

Volume | 34 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2014 |

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### Keywords

- Binary lattice
- Linear complexity
- Linear recursion
- Pseudorandomness
- Two dimensions

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Ramanujan Journal*,

*34*(2), 237-263. https://doi.org/10.1007/s11139-013-9500-4

**On linear complexity of binary lattices, II.** / Gyarmati, Katalin; Mauduit, Christian; Sárközy, A.

Research output: Contribution to journal › Article

*Ramanujan Journal*, vol. 34, no. 2, pp. 237-263. https://doi.org/10.1007/s11139-013-9500-4

}

TY - JOUR

T1 - On linear complexity of binary lattices, II

AU - Gyarmati, Katalin

AU - Mauduit, Christian

AU - Sárközy, A.

PY - 2014

Y1 - 2014

N2 - The linear complexity is an important and frequently used measure of unpredictably and pseudorandomness of binary sequences. In Part I of this paper, we extended this notion to two dimensions: we defined and studied the linear complexity of binary and bit lattices. In this paper, first we will estimate the linear complexity of a truly random bit (M,N)-lattice. Next we will extend the notion of k-error linear complexity to bit lattices. Finally, we will present another alternative definition of linear complexity of bit lattices.

AB - The linear complexity is an important and frequently used measure of unpredictably and pseudorandomness of binary sequences. In Part I of this paper, we extended this notion to two dimensions: we defined and studied the linear complexity of binary and bit lattices. In this paper, first we will estimate the linear complexity of a truly random bit (M,N)-lattice. Next we will extend the notion of k-error linear complexity to bit lattices. Finally, we will present another alternative definition of linear complexity of bit lattices.

KW - Binary lattice

KW - Linear complexity

KW - Linear recursion

KW - Pseudorandomness

KW - Two dimensions

UR - http://www.scopus.com/inward/record.url?scp=84900827358&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84900827358&partnerID=8YFLogxK

U2 - 10.1007/s11139-013-9500-4

DO - 10.1007/s11139-013-9500-4

M3 - Article

AN - SCOPUS:84900827358

VL - 34

SP - 237

EP - 263

JO - Ramanujan Journal

JF - Ramanujan Journal

SN - 1382-4090

IS - 2

ER -