# The Basic Algebra Behind Secret Codes and Space Communication

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2023-01-24 18:00:12

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.

Two students, Art and Zeke, are exchanging secret messages in Ms. Al-Jabr’s math class. Art unfolds Zeke’s latest note to reveal the numbers 57 and 99. He knows he has to supply the x-coordinates 3 and 6 to create the points (3, 57) and (6, 99). Art plugs each point into the linear equation y = Ax + B and produces the following system of equations: