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.

N1 - Funding Information:
This work has been supported by JSPS KAKENHI Grant-in-Aid for Scientific Research (A) Number 16H01723.
Publisher Copyright:
© 2018 Association for Computing Machinery.

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

T2 - 6th International Conference on Information Technology: IoT and Smart City, ICIT 2018

Y2 - 29 December 2018 through 31 December 2018

ER -