Probability of correcting errors

This article discusses the probability of correcting errors in error-correcting codes, using the Hadamard code from the Mariner 9 probe as an example. It explains how to calculate the probability that a certain number of bit flips occur, using the binomial cumulative distribution function. The article notes that the probability of successful correction is often higher than the simple lower bound, as not all error patterns are equally likely. It also covers how to determine the maximum bit error rate p that achieves a desired recovery probability, using the inverse of the regularized incomplete beta function. The content is technical, aimed at readers with some background in probability and coding theory, and includes Python code examples.