Year: 2011
Type: preprint
Abstract: Consider the set of all error--correcting block codes over a fixed alphabet with $q$ letters. It determines a recursively enumerable set of points in the unit square with coordinates $(R,δ)$:= {\it (relative transmission rate, relative minimal distance).} Limit points of this set form a closed subset, defined by $R\le α_q(δ)$, where $α_q(δ)$ is a continuous decreasing function called {\it asymptotic bound.} Its existence was proved by the author in 1981, but all attempts to find an explicit formula for it so far failed. In this note I consider the question whether this function is computable in the sense of constructive mathematics, and discuss some arguments suggesting that the answer might be negative.
Source: arXiv (Cornell University)
Author: Manin, Yuri I.
Institution: Max Planck Institute for Mathematics
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1943801288