Special Arcs in Projective Plane Over Galois Field of Order Sixteen
نویسندگان
چکیده
منابع مشابه
New arcs in projective Hjelmslev planes over Galois rings
It is known that some good linear codes over a finite ring (R-linear codes) arise from interesting point constellations in certain projective geometries. For example, the expurgated Nordstrom-Robinson code, a nonlinear binary [14, 6, 6]-code which has higher minimum distance than any linear binary [14, 6]-code, can be constructed from a maximal 2-arc in the projective Hjelmslev plane over Z4. W...
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It is shown that the maximal size of a 2-arc in the projective Hjelmslev plane over Z25 is 21, and the (21, 2)-arc is unique up to isomorphism. Furthermore, all maximal (20, 2)-arcs in the affine Hjelmslev plane over Z25 are classified up to isomorphism.
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In the Galois projective plane of square order q, we show the existence of small dense (k; 4)-arcs whose points lie on two conics for q odd, and on two hyperovals for q even. We provide an explicit construction of (4 √ q− 4; 2)-arcs for q even, and we also show that they are complete as far as q6 1024. c © 2002 Elsevier Science B.V. All rights reserved.
متن کاملNew complete 2 - arcs in the uniform projective Hjelmslev planes over chain rings of order 25
In this paper a 2-arc of size 21 in the projective Hjelmslev plane PHG(2,Z25) and a 2-arc of size 22 in PHG(2,F5[X]/(X)) are given. Both arcs are bigger than the 2-arcs previously known in the respective plane. Furthermore, we will give some information on the geometrical structure of the arcs.
متن کاملPolynomials over Galois Field
( ) [ ] [ ] ( ) 1 2 0 0 1 0 0 1 2 0 1 1 0 2 n m n m a b a b a b x a b a b a b x a b x + = ⋅ + ⋅ + ⋅ + ⋅ + ⋅ + ⋅ + + ⋅ . The coefficient operations are performed using the operations for the field from which the coefficients were taken. • Such a collection of polynomials forms a commutative ring with identity. • Nonzero field elements are considered to be zero-degree polynomials. The zero elemen...
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ژورنال
عنوان ژورنال: Journal of Physics: Conference Series
سال: 2021
ISSN: 1742-6588,1742-6596
DOI: 10.1088/1742-6596/1818/1/012176