A computability challenge: asymptotic bounds and isolated error-correcting codes

Details A computability challenge: asymptotic bounds and isolated error-correcting codes A computability challenge: asymptotic bounds and isolated error-correcting codes

2011-07-21

arxiv.org/abs/1107.4246v1

Computer Science

Information Theory

11 pages

Scientific paper

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 $(R,\delta)$:= {\it (relative transmission rate, relative minimal distance).} Limit points of this set form a closed subset, defined by $R\le \alpha_q(\delta)$, where $\alpha_q(\delta)$ 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.

Affiliated with

Also associated with

No associations

Rating

A computability challenge: asymptotic bounds and isolated error-correcting codes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A computability challenge: asymptotic bounds and isolated error-correcting codes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A computability challenge: asymptotic bounds and isolated error-correcting codes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-687813