On the $(4\nu,3)$-arcs in $PG(2,q)$ and the related linear codes

	On the $(4\nu,3)$-arcs in $PG(2,q)$ and the related linear codes
International Journal of Nonlinear Analysis and Applications
دوره 12، شماره 2، بهمن 2021، صفحه 2589-2599 اصل مقاله (141.02 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.5430
نویسندگان
Hanan J. Al_Mayyahi؛ Mohammed A. Alabbood^*
Department of Mathematics, College of Science, University of Basrah, Iraq
چکیده
In this paper, we use an irreducible plane-cubic curves in the projective plane $PG(2,q)$ to construct (k,3)-arcs of size $4\nu$ where $\lceil \frac{q+1-2\sqrt{q}}{4}\rceil\leq\nu\leq\lfloor \frac{q+1+2\sqrt{q}}{4} \rfloor$. Each of these arcs gives rise to an error-correcting code that corrects the maximum possible number of errors for its length. Furthermore, we discuss the completeness of each arc. The isotropy subgroup of each arc are determined. All Griesmer codes that correspond to plane-cubic curves are given for $7\leq q\leq 37,q$ is a prime.
کلیدواژه‌ها
Cubic curves؛ Arcs؛ Projective plane؛ codes؛ stabilizer groups
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