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

M. Arshad Ali; Yuta Kodera; Shoji Heguri; Takuya Kusaka; Satoshi Uehara; Robert H. Morelos-Zaragoza

doi:10.1145/3301551.3301562

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

M. Arshad Ali, Yuta Kodera, Shoji Heguri, Takuya Kusaka, Satoshi Uehara, Robert H. Morelos-Zaragoza

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

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
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	https://doi.org/10.1145/3301551.3301562
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

Conference

Conference	6th International Conference on Information Technology: IoT and Smart City, ICIT 2018
Country/Territory	Hong Kong
City	Hong Kong
Period	12/29/18 → 12/31/18

Keywords

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

ASJC Scopus subject areas

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

Access to Document

10.1145/3301551.3301562

Cite this

Arshad Ali, M., Kodera, Y., Heguri, S., Kusaka, T., Uehara, S., & Morelos-Zaragoza, R. H. (2018). Bit distribution of binary sequence generated by trace function and Legendre symbol over sub extension field. In 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.

ICIT 2018 - Proceedings of the 6th International Conference on Information Technology: IoT and Smart City. Association for Computing Machinery, 2018. p. 92-96 (ACM International Conference Proceeding Series).

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

Arshad Ali, M, Kodera, Y, Heguri, S, Kusaka, T, Uehara, S & Morelos-Zaragoza, RH 2018, Bit distribution of binary sequence generated by trace function and Legendre symbol over sub extension field. in 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

Arshad Ali M, Kodera Y, Heguri S, Kusaka T, Uehara S, Morelos-Zaragoza RH. Bit distribution of binary sequence generated by trace function and Legendre symbol over sub extension field. In ICIT 2018 - Proceedings of the 6th International Conference on Information Technology: IoT and Smart City. Association for Computing Machinery. 2018. p. 92-96. (ACM International Conference Proceeding Series). https://doi.org/10.1145/3301551.3301562

Arshad Ali, M. ; Kodera, Yuta ; Heguri, Shoji ; Kusaka, Takuya ; Uehara, Satoshi ; Morelos-Zaragoza, Robert H. / Bit distribution of binary sequence generated by trace function and Legendre symbol over sub extension field. ICIT 2018 - Proceedings of the 6th International Conference on Information Technology: IoT and Smart City. Association for Computing Machinery, 2018. pp. 92-96 (ACM International Conference Proceeding Series).

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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.",

keywords = "Legendre symbol, Primitive polynomial, Pseudo-random sequence, Sub extension field, Trace function",

author = "{Arshad Ali}, M. and Yuta Kodera and Shoji Heguri and Takuya Kusaka and Satoshi Uehara and Morelos-Zaragoza, {Robert H.}",

note = "Funding Information: This work has been supported by JSPS KAKENHI Grant-in-Aid for Scientific Research (A) Number 16H01723. Publisher Copyright: {\textcopyright} 2018 Association for Computing Machinery.; 6th International Conference on Information Technology: IoT and Smart City, ICIT 2018 ; Conference date: 29-12-2018 Through 31-12-2018",

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AU - Uehara, Satoshi

AU - Morelos-Zaragoza, Robert H.

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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.

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

Abstract

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Keywords

ASJC Scopus subject areas

Access to Document

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