Correction of Multiple Errors by $q$-ary Codes

We consider linear $(n, k)$-codes over $GF(q)$ capable of correcting $t$-fold errors in the insertion, erasure, and replacement metric. It is shown that their rate does not exceed 1/2. For $n\geq 2(k+t-1)$, a sufficient existence condition of such codes is derived. A direct construction is applied to verify this condition for $(4m, 2m)$-codes and $t=1$ with $q\geq 7$ and for $(6m, 2m)$-codes and $t=2$ with $q\geq 23$.