Nonexistence of some ternary linear codes with minimum weight-2 modulo 9

One of the fundamental problems in coding theory is to find n(q)(k, d), the minimum length n for which a linear code of length n, dimension k, and the minimum weight d over the field of order q exists. The problem of determining the values of n(q)(k, d) is known as the optimal linear codes problem. Using the geometric methods through projective geometry and a new extension theorem given by Kanda (2020), we determine n(3)(6, d) for some values of d by proving the nonexistence of linear codes with certain parameters.