Definition of Parameters of a Code

Let $n$, $M$, $d$, and $q$ be natural numbers. A code $C$ called an $(n,M,d{)}_q$-code when…

• the underlying alphabet used for $C$ has $q$ symbols,
• each codeword in $C$ has length $n$,
• $C$ itself has $M$ codewords in total, i.e. $M=|C|=\#C$, and
• $d$ is its minimal distance, i.e. $d=d_{\text{min}}(C)$.

These numbers $n$, $M$, $d$, and $q$ are called the parameters of $C$.

Note: if the number of symbols $q$ is not important in the context, we sometimes omit $q$ and simply say that $C$ is an $(n,M,d)$-code.