### Abstract

The authors of this paper have observed the distribution of bit patterns property of a binary sequence which is generated by using a primitive polynomial, trace function, and Legendre symbol over the sub extension field. However, one of the most important measure for evaluating the randomness of a sequence which is so called the distribution of bit patterns still has not been investigated. This paper focused on the distribution of bit patterns based on some experimental results. After observing many experimental results, the authors found that the number of appearance of each bit pattern is related to the number of zeros contained in each bit pattern. Furthermore, the authors formulated an equation to explain the distribution of bit patterns in a binary sequence.

Original language | English |
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Title of host publication | ICIT 2018 - Proceedings of the 6th International Conference on Information Technology |

Subtitle of host publication | IoT and Smart City |

Publisher | Association for Computing Machinery |

Pages | 92-96 |

Number of pages | 5 |

ISBN (Electronic) | 9781450366298 |

DOIs | |

Publication status | Published - Dec 29 2018 |

Event | 6th International Conference on Information Technology: IoT and Smart City, ICIT 2018 - Hong Kong, Hong Kong Duration: Dec 29 2018 → Dec 31 2018 |

### Publication series

Name | ACM International Conference Proceeding Series |
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### Conference

Conference | 6th International Conference on Information Technology: IoT and Smart City, ICIT 2018 |
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Country | Hong Kong |

City | Hong Kong |

Period | 12/29/18 → 12/31/18 |

### Fingerprint

### Keywords

- Legendre symbol
- Primitive polynomial
- Pseudo-random sequence
- Sub extension field
- Trace function

### ASJC Scopus subject areas

- Human-Computer Interaction
- Computer Networks and Communications
- Computer Vision and Pattern Recognition
- Software

### Cite this

*ICIT 2018 - Proceedings of the 6th International Conference on Information Technology: IoT and Smart City*(pp. 92-96). (ACM International Conference Proceeding Series). Association for Computing Machinery. https://doi.org/10.1145/3301551.3301562

**Bit distribution of binary sequence generated by trace function and Legendre symbol over sub extension field.** / Arshad Ali, M.; Kodera, Yuta; Heguri, Shoji; Kusaka, Takuya; Uehara, Satoshi; Morelos-Zaragoza, Robert H.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*ICIT 2018 - Proceedings of the 6th International Conference on Information Technology: IoT and Smart City.*ACM International Conference Proceeding Series, Association for Computing Machinery, pp. 92-96, 6th International Conference on Information Technology: IoT and Smart City, ICIT 2018, Hong Kong, Hong Kong, 12/29/18. https://doi.org/10.1145/3301551.3301562

}

TY - GEN

T1 - Bit distribution of binary sequence generated by trace function and Legendre symbol over sub extension field

AU - Arshad Ali, M.

AU - Kodera, Yuta

AU - Heguri, Shoji

AU - Kusaka, Takuya

AU - Uehara, Satoshi

AU - Morelos-Zaragoza, Robert H.

PY - 2018/12/29

Y1 - 2018/12/29

N2 - The authors of this paper have observed the distribution of bit patterns property of a binary sequence which is generated by using a primitive polynomial, trace function, and Legendre symbol over the sub extension field. However, one of the most important measure for evaluating the randomness of a sequence which is so called the distribution of bit patterns still has not been investigated. This paper focused on the distribution of bit patterns based on some experimental results. After observing many experimental results, the authors found that the number of appearance of each bit pattern is related to the number of zeros contained in each bit pattern. Furthermore, the authors formulated an equation to explain the distribution of bit patterns in a binary sequence.

AB - The authors of this paper have observed the distribution of bit patterns property of a binary sequence which is generated by using a primitive polynomial, trace function, and Legendre symbol over the sub extension field. However, one of the most important measure for evaluating the randomness of a sequence which is so called the distribution of bit patterns still has not been investigated. This paper focused on the distribution of bit patterns based on some experimental results. After observing many experimental results, the authors found that the number of appearance of each bit pattern is related to the number of zeros contained in each bit pattern. Furthermore, the authors formulated an equation to explain the distribution of bit patterns in a binary sequence.

KW - Legendre symbol

KW - Primitive polynomial

KW - Pseudo-random sequence

KW - Sub extension field

KW - Trace function

UR - http://www.scopus.com/inward/record.url?scp=85062901311&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85062901311&partnerID=8YFLogxK

U2 - 10.1145/3301551.3301562

DO - 10.1145/3301551.3301562

M3 - Conference contribution

AN - SCOPUS:85062901311

T3 - ACM International Conference Proceeding Series

SP - 92

EP - 96

BT - ICIT 2018 - Proceedings of the 6th International Conference on Information Technology

PB - Association for Computing Machinery

ER -