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  "body": "\n## Definition\n\nLet $n \\ge 1$ and let $S^{n-1} = \\set{x \\in \\R^n : x \\cdot x = 1}$ be the unit sphere, where $x \\cdot y$ is the [[dot product|0S52TNNTH9]].\nA *spherical code* in $\\R^n$ is a finite nonempty subset $C \\subset S^{n-1}$.\nLet $0 \u003c \\theta \\le \\pi$.\nThe code $C$ has *minimal angle* at least $\\theta$ if $x \\cdot y \\le \\cos \\theta$ for all distinct $x, y \\in C$.\nEquivalently, every two distinct points of $C$ make an [[angle|0ZEHZY85E6]] at least $\\theta$ at the origin.\nThe largest size of a spherical code in $\\R^n$ with minimal angle at least $\\theta$ is denoted $A(n, \\theta)$.\n\n## Remarks\n\nExample: the $2n$ points $\\pm e_1, \\dots, \\pm e_n$, where $e_i$ are the standard basis vectors, form a spherical code with minimal angle $\\pi/2$.\nTwo distinct points among them have dot product $0$ or $-1$, both at most $\\cos(\\pi/2) = 0$.\nNon-example: in $\\R^2$, the points $(1, 0)$, $(0, 1)$ and $(1/\\sqrt 2, 1/\\sqrt 2)$ do not have minimal angle at least $\\pi/2$, since the dot product of the first and the third is $1/\\sqrt 2 \u003e 0$.\nThe [[kissing number|B408FZYXF9]] is $\\tau(n) = A(n, \\pi/3)$.\n",
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