### Abstract

The distribution of bit patterns is an important measure to check the randomness of a sequence. The authors of this paper observed this crucial property in a binary sequence which generated by using a primitive polynomial, trace function, and Legendre symbol defined over the sub extension field. The authors create a new dimension in the sequence generation research area by considering the sub extension field, whereas all our previous works are focused in the prime field. In terms of distribution of bit patterns property, this research work has notable outcomes more specifically the binary sequence (defined over the sub extension field) holds much better (close to uniform) bit distribution than the previous binary sequence (defined over the prime field). Furthermore, the authors theoretically proved the distribution of bit property in this paper.

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

Pages (from-to) | 370-379 |

Number of pages | 10 |

Journal | Advances in Science, Technology and Engineering Systems |

Volume | 4 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jan 1 2019 |

### Fingerprint

### Keywords

- Distribution of bit patterns
- Legendre symbol
- Primitive polynomial
- Pseudo-random sequence
- Trace function

### ASJC Scopus subject areas

- Engineering (miscellaneous)
- Physics and Astronomy (miscellaneous)
- Management of Technology and Innovation

### Cite this

*Advances in Science, Technology and Engineering Systems*,

*4*(2), 370-379. https://doi.org/10.25046/aj040246

**Distribution of bit patterns in binary sequence generated over sub extension field.** / Ali, Md Arshad; Kodera, Yuta; Kusaka, Takuya; Nogami, Yasuyuki; Uehara, Satoshi; Morelos-Zaragoza, Robert H.

Research output: Contribution to journal › Article

*Advances in Science, Technology and Engineering Systems*, vol. 4, no. 2, pp. 370-379. https://doi.org/10.25046/aj040246

}

TY - JOUR

T1 - Distribution of bit patterns in binary sequence generated over sub extension field

AU - Ali, Md Arshad

AU - Kodera, Yuta

AU - Kusaka, Takuya

AU - Nogami, Yasuyuki

AU - Uehara, Satoshi

AU - Morelos-Zaragoza, Robert H.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - The distribution of bit patterns is an important measure to check the randomness of a sequence. The authors of this paper observed this crucial property in a binary sequence which generated by using a primitive polynomial, trace function, and Legendre symbol defined over the sub extension field. The authors create a new dimension in the sequence generation research area by considering the sub extension field, whereas all our previous works are focused in the prime field. In terms of distribution of bit patterns property, this research work has notable outcomes more specifically the binary sequence (defined over the sub extension field) holds much better (close to uniform) bit distribution than the previous binary sequence (defined over the prime field). Furthermore, the authors theoretically proved the distribution of bit property in this paper.

AB - The distribution of bit patterns is an important measure to check the randomness of a sequence. The authors of this paper observed this crucial property in a binary sequence which generated by using a primitive polynomial, trace function, and Legendre symbol defined over the sub extension field. The authors create a new dimension in the sequence generation research area by considering the sub extension field, whereas all our previous works are focused in the prime field. In terms of distribution of bit patterns property, this research work has notable outcomes more specifically the binary sequence (defined over the sub extension field) holds much better (close to uniform) bit distribution than the previous binary sequence (defined over the prime field). Furthermore, the authors theoretically proved the distribution of bit property in this paper.

KW - Distribution of bit patterns

KW - Legendre symbol

KW - Primitive polynomial

KW - Pseudo-random sequence

KW - Trace function

UR - http://www.scopus.com/inward/record.url?scp=85069794477&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85069794477&partnerID=8YFLogxK

U2 - 10.25046/aj040246

DO - 10.25046/aj040246

M3 - Article

VL - 4

SP - 370

EP - 379

JO - Advances in Science, Technology and Engineering Systems

JF - Advances in Science, Technology and Engineering Systems

SN - 2415-6698

IS - 2

ER -