This chapter considers two fundamental questions for detecting and correcting errors made while playing the card game SET®. The game is played with a special deck of eighty-one cards, and the objective is to find three cards that form a set. Over the course of a game, a player may make a mistake by taking three cards that do not form a set—a common occurrence which this chapter examines by first introducing coordinates for the cards and then uses these coordinates to define a Hamming weight for any subset of cards. The chapter then uses the facts about Hamming weight to describe a variant of the game, called the EndGame, which leads to error detection. Afterward, the chapter produces a perfect, single-error-correcting linear code solely from SET® cards. It concludes with additional topics that demonstrate the deep connections between the simple card game and advanced mathematics.
Single-Error Detection and Correction for Duplication and Substitution Channels
