Nonexistence Of Some Ternary Linear Codes

We prove the nonexistence of some ternary linear codes of dimension 6, which implies that n(3)(6, d) = g(3)(6, d) + 2 for d = 48, 49, 66, 67, 149, 150, where g(3)(k, d) = Sigma(k-1)(i=0) inverted right perpendiculard/3(i)inverted left perpendicular and n(q)(k, d) denotes the minimum length n for which an [n, k, d](q) code exists. To prove the nonexistence of a putative code through projective geometry, we introduce some proof techniques such as i-Max and i-Max-NS to rule out some possible weights of codewords. (C) 2021 Elsevier B.V. All rights reserved.