Summary: The \(m\)-adic residue codes are a generalization of the quadratic residue codes. They are cyclic codes which exist at prime lengths \(p\) over \(GF(q)\) when \(m\mid (p-1),(q,p)=1\), and \(q\) is an \(m\)-adic residue modulo \(p\). The \(m\)-adic residue codes are investigated and are found to have many of the strong properties of the quadratic residue codes. A subgroup of the automorphism group and restrictions on the form of the idempotents of the \(m\)-adic residue codes are given. It is shown that some \(m\)-adic residue codes are self-orthogonal and the duals of some \(m\)-adic residue codes are their complements. Bounds on the minimum of the weights of the odd-like vectors in the odd-like codes are given. (For binary codes, this is the minimum odd weight.) At some lengths, \(m\)-adic residue codes exist for several values of \(m\). Containment relationships between these codes are demonstrated which show that when \(m\) is even, \(m\)-adic residue codes inherit properties of quadratic residue codes. A table is included that contains minimum weights of the binary \(m\)-adic residue codes of lengths less than or equal to 127. Many of these codes have the highest possible minimum weight known for codes of their lengths and dimensions.