TY - JOUR
AU - Karapetyan, Karen I.
PY - 2022/06/01
Y2 - 2022/12/06
TI - Complete Caps in Affine Geometry AG(n, 3)
JF - Mathematical Problems of Computer Science
JA - MPCS
VL - 57
IS -
SE - Articles
DO - 10.51408/1963-0087
UR - http://mpcs.sci.am/index.php/mpcs/article/view/735
SP - 56–64
AB - <p>We consider the problem of constructing complete caps in affine geometry <em>AG</em>(<em>n</em>, 3) of dimension n over the field <em>F</em><sub>3</sub> of order three. We will take the elements of <em>F</em><sub>3</sub> to be 0, 1 and 2. A cap is a set of points, no three of which are collinear. Using the concept of <em>P<sub>n</sub></em> - set, we give two new methods for constructing complete caps in affine geometry <em>AG</em>(<em>n</em>, 3). These methods lead to some new upper and lower bounds on the possible minimal and maximal cardinality of complete caps in affine geometry <em>AG</em>(<em>n</em>, 3).</p>
ER -