New ternary linear codes from projectivity groups

In this note, the existence of [66,10,36]3[66,10,36]3 and [55,15,24]3[55,15,24]3 linear codes is proven. These ternary codes are constructed from orbits of a projectivity group of PG(k−1,F3)PG(k−1,F3), for k=10,15k=10,15. These new codes and their punctured subcodes improve the best known lower bounds on the largest possible minimum distance.