Using latin squares to understand hamming codes
George Bricker · Journal of computing sciences in colleges · 2012
Determining the codeword length, k, in order to correct a given number of bit errors is a relatively simple algorithm. However, choosing the correct q-ary subset of codewords from the 2^k set of possible codewords is not a trivial exercise. This tends to be the missing step in most textbooks and discussions of the Hamming bound. Using a set of Latin squares to represent the Hamming distance between all possible codewords provides a simpler, and more visual, representation of k-space, and provides a method for choosing acceptable codewords. Moreover, a Latin squares approach can prove useful for discussing many types of error-detection and error correction.