equivalent codes:
If C1 and C2 are two codes of length n and if there is a permutation p in Sn for which (c1,...,cn) in C1 if and only if (cp(1),...,cp(n)) in C2, then we say C1 and C2 are permutation equivalent. In more generality, if there is an n x n monomial matrix M : Fn --> Fn which sends C1 isomorphically to C2 then we say C1 and C2 are equivalent.
Extended code:
Suppose C is an [n,k,d] code over GF(q). An extended code C^ is a code of length n+1 of the form
{ (c1,...,cn,cn+1) in GF(q)n+1 | (c1,...,cn) in C and cn+1 = c • a }
for some fixed (non-zero) vector a in GF(q)n. Here • refers to the standard inner product on GF(q)n.