Caps and codes
نویسندگان
چکیده
منابع مشابه
Binary Codes and Caps
The connection between maximal caps (sometimes called complete caps) and certain binary codes called quasi-perfect codes is described. We provide a geometric approach to the foundational work of Davydov and Tombak who have obtained the exact possible sizes of large maximal caps. A new self-contained proof of the existence and the structure of the largest maximal nonaffine cap in PG(n, 2) is giv...
متن کاملCodes in spherical caps
We consider bounds on codes in spherical caps and related problems in geometry and coding theory. An extension of the Delsarte method is presented that relates upper bounds on the size of spherical codes to upper bounds on codes in caps. Several new upper bounds on codes in caps are derived. Applications of these bounds to estimates of the kissing numbers and one-sided kissing numbers are consi...
متن کاملCodes and caps from orthogonal Grassmannians
In this paper we investigate linear error correcting codes and projective caps related to the Grassmann embedding ε k of an orthogonal Grassmannian ∆k. In particular, we determine some of the parameters of the codes arising from the projective system determined by ε k (∆k). We also study special sets of points of ∆k which are met by any line of ∆k in at most 2 points and we show that their imag...
متن کاملSemidefinite programming, multivariate orthogonal polynomials, and codes in spherical caps
In this paper we apply the semidefinite programming approach developed in [2] to obtain new upper bounds for codes in spherical caps. We compute new upper bounds for the one-sided kissing number in several dimensions where we in particular get a new tight bound in dimension 8. Furthermore we show how to use the SDP framework to get analytic bounds. Dedicated to Eiichi Bannai in occasion of his ...
متن کاملLong Binary Linear Codes and Large Caps in Projective Space
We obtain, in principle, a complete classification of all long inextendable binary linear codes. Several related constructions and results are presented.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1978
ISSN: 0012-365X
DOI: 10.1016/0012-365x(78)90120-6