Minimum distance of a code ($d(C)$)

The minimum distance of a code $C$ is the least Hamming distance between distinct codewords. For a linear code, translation invariance makes this equal to the least Hamming weight of a nonzero codeword.

The relative minimum distance of a length-$n$ code of minimum distance $d$ is $d/n$. It expresses the guaranteed separation as a fraction of the block length.

// Target: algebra.bigb

The quantity $A_q(n,d)$ is the largest cardinality of a length-$n$ code over an alphabet of size $q$ with minimum Hamming distance at least $d$. The code need not be linear.

// Target: algebra.bigb