Sharp groups, two-weight codes and maximal arcs
نویسندگان
چکیده
منابع مشابه
Groups of Maximal Arcs
Apart from hyperovals and their duals there are only three classes of maximal arcs known in Desarguesian projective planes. Two classes are due to J. A. Thas and one to R. H. F. Denniston. In this paper collineation stabiliser and isomorphism problems for those maximal arcs in Desarguesian projective planes are examined. The full collineation stabilisers of the known maximal arcs are calculated...
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We are interested in the construction of linear [n, k; q] two-weight codes. A linear code is a k−dimensional subspaceC of the n−dimensional vector spaceGF (q) over the finite fieldGF (q) with q elements. The q codewords of length n are the elements of the subspace, they are written as row vectors. The weight of a codeword c is the number of nonzero components of the vector c ∈ GF (q). In the ca...
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We construct an infinite family of two-Lee-weight and three-Lee-weight codes over the non-chain ring Fp+uFp+ vFp+uvFp, where u 2 = 0, v = 0, uv = vu. These codes are defined as trace codes. They have the algebraic structure of abelian codes. Their Lee weight distribution is computed by using Gauss sums. With a linear Gray map, we obtain a class of abelian three-weight codes and two-weight codes...
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The triple factorization of a group $G$ has been studied recently showing that $G=ABA$ for some proper subgroups $A$ and $B$ of $G$, the definition of rank-two geometry and rank-two coset geometry which is closely related to the triple factorization was defined and calculated for abelian groups. In this paper we study two infinite classes of non-abelian finite groups $D_{2n}$ and $PSL(2,2^{n})$...
متن کاملAlgebraic curves and maximal arcs
A lower bound on the minimum degree of the plane algebraic curves containing every point in a large point-set K of the Desarguesian plane PG(2, q) is obtained. The case where K is a maximal (k, n)-arc is considered in greater depth.
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2008
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2006.12.002