Optimal Ternary $11,7$ and $14,10$ Error-Correcting Codes

Abstract

We use exhaustive computer searches to show that there are exactly $36$ codewords in an optimal ternary $(11,7)$ code and exactly $13$ codewords in an optimal ternary $(14,10)$ code. We also enumerate inequivalent optimal ternary $(14,10)$ codes and show that there are exactly $6151$ such codes.