Nonexistence of linear codes meeting the Griesmer bound

作者：Ma, Wen; Luo, Jinquan^*

来源：Discrete Mathematics, 2022, 345(4): 112744.

DOI：10.1016/j.disc.2021.112744

• Griesmer bound
• Minihyper
• Spectrum
• Arcs

In this paper, we prove the nonexistence of [g(q)(5, d), 5, d](q) codes for q(4) - 3q(2) - q + 1 <= d <= q(4) - 3q(2) and q(4) - 2q(2) - 3q + 3 <= d <= q(4) - 2q(2) - 2q with q >= 5. We also prove the nonexistence of [g(q)(4,d),4,d](q) codes for 2q(3) - rq(2) - 3q +1 <= d <= 2q(3) - rq(2) with 3 <= r <= q-1 2 and q >= 7.