The Basic Algebra Behind Secret Codes and Space Communication — Quanta Magazine

How can you use systems of linear equations to send secret messages? Just do what NASA does! In my latest column for Quanta Magazine I explore the school math behind Reed-Solomon codes, which are used to safely and securely send data across the solar system.

Space exploration requires tremendous precision. When you’re landing a rover on Mars 70 million miles away from the nearest service station, you need to maximize efficiency and prepare for the unexpected. This applies to everything from spacecraft design to data transmission: Those messages returning to Earth as a steady stream of 0s and 1s are bound to contain some errors, so you need to be able to identify and correct them without wasting precious time and energy.

That’s where math comes in. Mathematicians have invented ingenious ways to transmit and store information. One surprisingly effective method uses Reed-Solomon codes, which are built on the same basic algebra that students learn in school. Let’s drop in on a math class to see how Reed-Solomon codes help transmit and secure information while correcting any costly errors that pop up.

The full article is freely available is here.