On optimal ternary linear codes of dimension 6
Tatsuya Maruta, Yusuke Oya · Advances in Mathematics of Communications · 2011
We prove that $[g_3(6,d),6,d]_3$ codes for$d=253$-$267$ and $[g_3(6,d)+1,6,d]_3$ codes for$d=302, 303, 307$-$312$ exist and that$[g_3(6,d),6,d]_3$ codes for$d=175, 200, 302, 303, 308, 309$ and a $[g_3(6,133)+1,6,133]_3$ codedo not exist,where $g_3(k,d)=\sum_{i=0}^{k-1} \lceil d / 3^i \rceil$.These determine $n_3(6,d)$ for $d=133, 175, 200, 253$-$267,302, 303, 308$-$312$, where $n_q(k,d)$ is the minimum length $n$ for whichan $[n,k,d]_q$ code exists.The updated $n_3(6,d)$ table is also given.