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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 | ||
| تاریخ دریافت: 10 فروردین 1400، تاریخ بازنگری: 22 اردیبهشت 1400، تاریخ پذیرش: 06 تیر 1400 | ||
| 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 | ||
| مراجع | ||
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