Curve Interpolation and Coding Theory

Whether it is downloading files from the Internet, having conversations between cell phones, or sending information from a laptop to a printer, we often want to transmit data in situations where we need to worry about interference from other signals that may cause errors in the transmission.

The branch of mathematics known as coding theory is dedicated to finding ways to tell when there are errors in transmission and, when possible, how to correct those errors. The goal of coding theory is to build as much redundancy as possible into a message without greatly increasing its length. Much of coding theory uses deep mathematics to achieve this end, but a surprising amount of work follows from the following fact of Euclidean geometry, which is known by schoolchildren: