That's a fantastic introduction (although it's far more than an introduction!). I wrote a native addon for Node.js that does Reed Solomon, also using optimized Cauchy matrices (MIT license): https://github.com/ronomon/reed-solomon
Thanks. If that was in November last year, then it's changed a lot since then (and now a few times faster). Back then it was using a Vandermonde matrix as it was based on Backblaze's Java implementation, but a month ago everything was rewritten to use optimized Cauchy matrices.
Until recently I worked for a molecular neurobiology research group that, among other things, used Single-molecule RNA Fluorescence in situ Hybridization (smFISH) to measure gene expression in tissue[0].
Basically: design viruses with fluorescent molecules attached to them such that they attach to specific sections of RNA in the cell that are associated with particular genes. Soak tissue in viruses. Look at tissue through a microscope and count individual fluorescent dots, each of which represents one RNA molecule (I find this absolutely mind-blowing). Wash off the viruses with a specific type of chemical, and repeat with a new one for a different gene.
You can only use a few colours at a time because otherwise the microscope cannot discern them. But that would severely limit the throughput - there are a lot of genes we want to check, but the tissue will also degenerate after repeated washing. So, what can we do? Well, as I've understood, scientists using smFISH and similar techniques now use multiplexing and with Hamming codes to get around that.
So yeah, linear algebra is definitely so, so hot right now.
