abstract
We denote by m r,q(s) the minimum value of f for which an {f, θr-2+s ; r,q }-minihyper exists for r ≥ 3, 1 ≤ s ≤ q−1, where θ j =(q j+1−1)/(q−1). It is proved that m 3,q (s)=θ1(θ1+s) for many cases (e.g., for all q ≥ 4 when \(s \le {\sqrt q}-1\) ) and that m r,q(s) ≥ θr-1+sθ1+q for 1 ≤ s ≤ q − 1,~q ≥ 3,~r ≥ 4. The nonexistence of some [n,k,n+s−q k-2] q codes attaining the Griesmer bound is given as an application.
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D. Jungnickel
AMS classification: 94B27, 94B05, 51E22, 51E21
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Maruta, T., Landjev, I.N. & Rousseva, A. On the Minimum Size of Some Minihypers and Related Linear Codes. Des Codes Crypt 34, 5–15 (2005). https://doi.org/10.1007/s10623-003-4191-2
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DOI: https://doi.org/10.1007/s10623-003-4191-2