球形码的渐近界
Asymptotic bounds for spherical codes
摘要：
基数为q的固定有限字母表F上的所有纠错码C的集合确定了具有坐标（R（C），delta（C））：=（相对传输速率，相对最小距离）的单位正方形中的码点集合。这种编码理论的核心问题在于同时最大化编码的传输速率和两个不同码字之间的相对最小汉明距离。在大量的文献中探索这个问题的经典方法包括发明明确的“好代码”的结构，并将新的代码类别与早期的代码进行比较。不太经典的方法研究的几何形状的整个代码点（R，三角洲）（与q固定），在第一次独立的可计算性的属性，只有afterwords转向问题的可计算性，类比与统计物理学等，本文的主要目的是在扩展这后者的战略领域的球形代码。
英文摘要：
The set of all error-correcting codes C over a fixed finite alphabet F of cardinality q determines the set of code points in the unit square with coordinates (R(C), delta (C)):= (relative transmission rate, relative minimal distance). The central problem of the theory of such codes consists in maximizing simultaneously the transmission rate of the code and the relative minimum Hamming distance between two different code words. The classical approach to this problem explored in vast literature consists in the inventing explicit constructions of "good codes" and comparing new classes of codes with earlier ones. Less classical approach studies the geometry of the whole set of code points (R,delta) (with q fixed), at first independently of its computability properties, and only afterwords turning to the problems of computability, analogies with statistical physics etc. The main purpose of this article consists in extending this latter strategy to domain of spherical codes.
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