New ternary linear codes from projectivity groups

In this note, the existence of [ 66 , 10 , 36 ] 3 and [ 55 , 15 , 24 ] 3 linear codes is proven. These ternary codes are constructed from orbits of a projectivity group of P G ( k − 1 , F 3 ) , for k = 10 , 15 . These new codes and their punctured subcodes improve the best known lower bounds on the largest possible minimum distance.