On the Nonexistence of Ternary $[284,6,188]$ Codes

Let $[n,k,d]_q$ codes be linear codes of length $n$, dimension $k$, and minimum Hamming distance $d$ over $GF(q)$. Let $n_q(k,d)$ be the smallest value of $n$ for which there exists an $[n,k,d]_q$ code. It is known from [1, 2] that $284\leq n_3(6,188)\leq 285$ and $285\leq n_3(6,189)\leq 286$. In this paper, the nonexistence of $[284,6,118]_3$ codes is proved, whence we get $n_3(6,118)=285$ and $n_3(6,189)=286$.