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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2024.9
- 수록면
- 1,161 - 1,173 (13page)
- DOI
- 10.4134/BKMS.b230115
이용수
초록· 키워드
오류제보하기
{O. Geil, F. \"Ozbudak, and D. Ruano give a construction of a sequence of length $(q-1)(q^{2}-1)$ with high nonlinear complexity by using a function on a Hermitian curve over $F_{q^{2}}$ with the pole divisor $ (q-1)P_{\infty}+(q-1)Q,$ where $ P_{\infty}$ is the point at infinity, $Q$ is a rational point with the order of its orbit is $q^2-1$ and $q$ is a prime power. They give lower bounds on the $k-$th ordered nonlinear complexities $N^{k}(s)$ and $L^{k}(s)$ on the Hermitian curve. In this work, we examine the lower bounds on $N^{k}(s)$ and $L^{k}(s)$ using all possible pairs of rational points that can be selected on a Hermitian curve over $F_{q^{2}}.$ In particular, we improve the bounds on $N^{k}(s)$ and $L^{k}(s)$ obtained by O. Geil, F. \"Ozbudak, and D. Ruano.}
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