Structure of functional codes defined on non-degenerate Hermitian varieties
نویسندگان
چکیده
منابع مشابه
New informations on the structure of the functional codes defined by forms of degree h on non - degenerate Hermitian varieties in P n ( F q )
We study the functional codes of order h defined by G. Lachaud on X ⊂ P(Fq) a nondegenerate Hermitian variety. We give a condition of divisibility of the weights of the codewords. For X a non-degenerate Hermitian surface, we list the first five weights and the corresponding codewords and give a positive answer on a conjecture formulated on this question. The paper ends with a conjecture on the ...
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We study the functional codes of second order defined by G. Lachaud on X ⊂ P(Fq) a quadric of rank(X )=3,4,5 or a non-degenerate hermitian variety. We give some bounds for the number of points of quadratic sections of X , which are the best possible and show that codes defined on non-degenerate quadrics are better than those defined on degenerate quadrics. We also show the geometric structure o...
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We investigate the functional code Ch(X) introduced by G. Lachaud [10] in the special case where X is a non-singular Hermitian variety in PG(N, q2) and h = 2. In [4], F. Edoukou solved the conjecture of Sørensen [11] on the minimum distance of this code for a Hermitian variety X in PG(3, q2). In this paper, we will answer the question about the minimum distance in general dimension N , with N <...
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This article studies the small weight codewords of the functional code CHerm(X), with X a non-singular Hermitian variety of PG(N, q2). The main result of this article is that the small weight codewords correspond to the intersections of X with the singular Hermitian varieties of PG(N, q2) consisting of q + 1 hyperplanes through a common (N −2)-dimensional space Π, forming a Baer subline in the ...
متن کاملThe weight distribution of the functional codes defined by forms of degree 2 on hermitian surfaces
We study the functional codes C2(X) defined on a projective variety X, in the case where X ⊂ P is a non-degenerate hermitian surface. We first give some bounds for #XZ(Q)(Fq), which are better than the ones known. We compute the number of codewords reaching the second weight. We also estimate the third weight, show the geometrical structure of the codewords reaching this third weight and comput...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2011
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2011.05.006