Some New Maximal Codes over $GF(4)$

For lengths $n\geq 5$ the authors construct linear codes over $GF(4)$ that correct two errors and have maximum possible numbers (from the standpoint of the Hamming bound) of information symbol $k$. The first nontrivial example of these new codes is a 4-ary ($n=11$, $k=6$, $d=5$) code. Its extension is a $(12,6,6)$ code and is interesting in that changing over to the binary form of elements of $GF(4)$ yields a $(24,12,8)$ Golay code. Thus this unique code can be represented in cascade form.