On the Minimum Size of Some Minihypers and Related Linear Codes |
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| Authors: | Email author" target="_blank">Tatsuya?MarutaEmail author Ivan?N?Landjev Assya?Rousseva |
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| Institution: | (1) Department of Applied Mathematics, Osaka Women s University, Daisen-cho, Sakai, Osaka 590-0035, Japan;(2) Institute of Mathematics, Bulgarian Academy of Sciences, 8 Acad. G. Bonchev str, Sofia, 1113, Bulgaria;(3) Faculty of Mathematics and Informatics, Sofia University, 5 J. Bourchier Blvd, 1126 Sofia, Bulgaria |
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| Abstract: | We denote by mr,q(s) the minimum value of f for which an {f,  r-2+s ; r,q }-minihyper exists for r  3, 1  s q–1, where j=(qj+1–1)/(q–1). It is proved that m3,q(s)=1(1+s) for many cases (e.g., for all q 4 when
) and that mr,q(s) r-1+s1+q for 1 s q – 1,~q 3,~r 4. The nonexistence of some n,k,n+s–qk-2]q codes attaining the Griesmer bound is given as an application.AMS classification: 94B27, 94B05, 51E22, 51E21 |
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| Keywords: | minihypers projective spaces linear codes Griesmer bound |
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