Abstract
We prove that there does not exist a [q4+q3−q2−3q−1, 5, q4−2q2−2q+1] q code over the finite field \(\mathbb{F}_q\) for q≥ 5. Using this, we prove that there does not exist a [g q (5, d), 5, d] q code with q4 −2q2 −2q +1 ≤ d ≤ q4 −2q2 −q for q≥ 5, where g q (k,d) denotes the Griesmer bound.
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MSC 2000: 94B65, 94B05, 51E20, 05B25
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Cheon, E.J., Kato, T. & Kim, S.J. Nonexistence of [n, 5, d] q Codes Attaining the Griesmer Bound for q4 −2q2 −2q+1 ≤ d≤ q4−2q2 −q. Des Codes Crypt 36, 289–299 (2005). https://doi.org/10.1007/s10623-004-1720-6
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DOI: https://doi.org/10.1007/s10623-004-1720-6