Özbudak, Ferruh and Tutaş, Nesrin (2024) Nonlinear complexity and weierstrass semigroup of two rational points on a Hermitian curve. Bulletin of the Korean Mathematical Society, 61 (5). pp. 1161-1173. ISSN 1015-8634 (Print) 2234-3016 (Online)
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Official URL: https://dx.doi.org/10.4134/BKMS.b230115
Abstract
O. Geil, F. Özbudak, and D. Ruano give a construction of a sequence of length (q − 1)(q2 − 1) with high nonlinear complexity by using a function on a Hermitian curve over Fq 2 with the pole divisor (q − 1)P∞ + (q − 1)Q, where P∞ is the point at infinity, Q is a rational point with the order of its orbit is q2 − 1 and q is a prime power. They give lower bounds on the k−th ordered nonlinear complexities Nk (s) and Lk (s) on the Hermitian curve. In this work, we examine the lower bounds on Nk (s) and Lk (s) using all possible pairs of rational points that can be selected on a Hermitian curve over Fq 2. In particular, we improve the bounds on Nk (s) and Lk (s) obtained by O. Geil, F. Özbudak, and D. Ruano.
Item Type: | Article |
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Uncontrolled Keywords: | Hermitian function field; nonlinear complexity; Weierstrass semigroup |
Divisions: | Faculty of Engineering and Natural Sciences |
Depositing User: | Ferruh Özbudak |
Date Deposited: | 20 Dec 2024 15:43 |
Last Modified: | 20 Dec 2024 15:43 |
URI: | https://research.sabanciuniv.edu/id/eprint/50541 |