Open AccessTwisted Hessian curves over the Ring F
Author(s) -
Elhamam Moha Ben Taleb,
Abdelhakim Chillali,
Lhoussain El Fadil
Publication year - 2022
Publication title -
boletim da sociedade paranaense de matemática
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.347
H-Index - 15
eISSN - 2175-1188
pISSN - 0037-8712
DOI - 10.5269/bspm.51867
Subject(s) - hessian matrix , bijection , mathematics , combinatorics , hessian equation , ring (chemistry) , projection (relational algebra) , prime (order theory) , prime power , mathematical analysis , algorithm , differential equation , chemistry , organic chemistry , first order partial differential equation
Let Fq[e] be a nite eld of q elements, where q is a power of a prime number p. In this paper, we study the Twisted Hessian curves over the ring Fq[e], where e2 = e, denoted by Ha,d(Fq[e]); (a,d) ∈ (Fq[e])2. Using the Twisted Hessian equation, we dene the Twisted Hessian curves Ha,d(Fq[e]) and we will show that Hπ0(a),π0(d)(Fq) and Hπ1(a),π1(d)(Fq) are two Twisted Hessian curves over the eld Fq, where π0 and π1 are respectively the canonical projection and the sum projection of coordinates from Fq[e] to Fq. Precisely, we give a bijection between the sets Ha,d(Fq[e]) and Hπ0(a),π0(d)(Fq)×Hπ1(a),π1(d)(Fq).