Computability on subsets of Euclidean space I: closed and compact subsets
Theoretical Computer Science - Special issue on computability and complexity in analysis
Recursively enumerable reals and Chaitin &OHgr; numbers
Theoretical Computer Science
Algebraic-Geometric Codes
Computability on subsets of metric spaces
Theoretical Computer Science - Topology in computer science
Plottable Real Number Functions and the Computable Graph Theorem
SIAM Journal on Computing
Algebraic Geometric Codes: Basic Notions
Algebraic Geometric Codes: Basic Notions
Random codes: minimum distances and error exponents
IEEE Transactions on Information Theory
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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):= (relative transmission rate, relative minimal distance). Limit points of this set form a closed subset, defined by R≤αq (δ), where αq (δ) is a continuous decreasing function called 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.