Block code

A code defined on a block of \(n\) symbols, with each symbol taken from some fixed possibly infinite alphabet \(\Sigma\) [1; Ch. 3]. Such alphabets include bits, Galois fields, rings, or real numbers, and the overall alphabet of the code is \(\Sigma^n\). In this context, \(n\) is called the length of the code. In some cases, there are conditions on which length-\(n\) strings are available to the codes. For example, in the case of spherical codes, one is constrained to \(n\)-dimensional real vectors on the unit sphere.

An alternative more stringent definition (not used here) is in terms of a map encoding logical information from \(\Sigma^k\) into \(\Sigma^n\), yielding an \((n,k,d)_{\Sigma}\) block code, where \(d\) is the code distance.