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Additional Information:
Կարապետյան, Կարեն Ի․, Карапетян Карен И.
Title:
Complete Caps in Affine Geometry AG(n, 3)
Other title:
Լրիվ գլխարկներ AG(n, 3) աֆինական երկրաչափությունում ; Полные шапки в аффинной геометрии AG(n, 3)
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Subject:
Mathematical cybernetics ; Computer science
Uncontrolled Keywords:
Affine geometry ; Projective geometry ; Cap ; Complete cap
Abstract:
We consider the problem of constructing complete caps in affine geometry AG(n, 3) of dimension n over the field f3 of order three. We will take the elements of f3 to be 0, 1 and 2. A cap is a set of points, no three of which are collinear. Using the concept of Pn−set, we give two new methods for constructing complete caps in affine geometry AG(n, 3). These methods lead to some new upper and lower bounds on the possible minimal and maximal cardinality of complete caps in affine geometry AG(n, 3).