Determine the parameters for any Hamming code over $\mathbb{F}_q$.

Question

Determine the parameters for any Hamming code over $\mathbb{F}_q$.

I am new to Coding Theory. I’m confused what "the parameters" exactly mean. What specifically am I supposed to determine?

Answer 1

The parameters are the length of the code , minimum distance and dimension

Definition . (Linear codes) $A$ code $C$ is a linear code if it is a subspace of the vector space $F_q^{n}$ of dimension $n$ over the field $GF(q)$.

If $C$ has dimension $k$ over $GF(q)$, we say that C is an $[n; k]$-code, and

If $C$ has the minimum distance $d$ we say $C$ is an $[n; k; d]$-code