Codes in spherical caps
نویسندگان
چکیده
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 considered. It is proved that the maximum size of codes in spherical caps for large dimensions is determined by the maximum size of spherical codes, so these problems are asymptotically equivalent.
منابع مشابه
ar X iv : m at h / 06 06 73 4 v 1 [ m at h . M G ] 2 8 Ju n 20 06 CODES 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 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 کاملRigidity of spherical codes
A packing of spherical caps on the surface of a sphere (that is, a spherical code) is called rigid or jammed if it is isolated within the space of packings. In other words, aside from applying a global isometry, the packing cannot be deformed. In this paper, we systematically study the rigidity of spherical codes, particularly kissing configurations. One surprise is that the kissing configurati...
متن کاملPacking and Minkowski Covering of Congruent Spherical Caps
Let Ci (i = 1, ..., N) be the i-th open spherical cap of angular radius r and let Mi be its center under the condition that none of the spherical caps contains the center of another one in its interior. We consider the upper bound, rN (not the lower bound!) of r of the case in which the whole spherical surface of a unit sphere is completely covered with N congruent open spherical caps under the...
متن کاملPolynomial approximation and quadrature on geographic rectangles
Using some recent results on subperiodic trigonometric interpolation and quadrature, and the theory of admissible meshes for multivariate polynomial approximation, we study product Gaussian quadrature, hyperinterpolation and interpolation on some regions of Sd, d ≥ 2. Such regions include caps, zones, slices and more generally spherical rectangles defined by longitudes and (co)latitudes (geogra...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Adv. in Math. of Comm.
دوره 1 شماره
صفحات -
تاریخ انتشار 2007