The New Turing Omnibus Chapter 12 Error Correcting Codes
Leo explains the Hadamard matrix and how to build successive ones from H1 using the Cartesian product:
Leo explains why the Hadamard matrix is particularly well-suited for picking code words for use in error correction as each row has a large difference between all others:
Leo demonstrates his browser-based visualisation of various Hadamard matrices:
We then used the H3 Hadamard matrix to pick a message (the number 5) and flip one bit and attempt to recover it.
We counted the number of errors between our corrupted message and each row to determine the correct code:
Leo explaining how many errors various Hadamard matrices can tolerate:
Our attempt to generate a matrix for 6-bit words:
- Leo's visualisation of the Hadamard matrix
- Leo's Reed-Muller encoder/decoder
- Leo's noisy: "a command-line utility that injects a customisable amount of random noise into a stream of bytes coming from standard input"
- James' noise-proxy: "a TCP proxy with configurable noise in both directions"
- Kevin's noisy_proxy
- Tom's implementation of Hadamard matrices in Ruby
Thanks to Leo and Geckoboard for both hosting and shepherding the meeting and to James C, Tom and Kevin for the software they wrote before the meeting.