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Minimum template groups in PG(2,q) and finding minimum template groups size 16&17 in PG(2,9) | ||
| Journal of Education and Science | ||
| Article 46, Volume 22, Issue 2, 2009, Pages 370-384 PDF (0 K) | ||
| DOI: 10.33899/edusj.2009.57688 | ||
| Authors | ||
| Chanar Abdulkareem Ahmed; AbdulKhlaq Lazem Yaseen | ||
| Abstract | ||
| Abstract A t – blocking set B in a projective plane PG(2, q) is a set of points such that each line in PG(2, q) contains at least t points of B and some line contains exactly t points of B. A t – blocking set B is minimal or irreducible when no proper subset of it is a t – blocking set. In particular when t = 1 then B is called a blocking set. In this paper, we find the lower bounds of the 5 – blocking set and the 6–blocking set In the projective plane PG(2, q), where q square, Then we improved the lower bound of 5– blocking set when in the same plane. Specially in the projective plane PG(2, 9): First: We show that the minimal blocking set of size 16 with a 6 – secant and the minimal blocking set of the same size of Rédei-type exist. Second: We classify the minimal blocking sets of size 17. | ||
| Keywords | ||
| template groups PG(2; q); minimum; 16&17 PG(2; 9) | ||
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