01036209

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01036209 Maruta, Tatsuya On the minimum length of $q$-ary linear codes of dimension five. Geom. Dedicata 65, No.3, 299-304 (1997). 1997 Springer, Dordrecht EN linear code minihyper Hamming distance lower bound Griesmer bound

doi:10.1023/A:1004901203236

A fundamental problem in coding theory is to determine $n_q (k,d)$, the minimum value of $n$ for which there exists an $[n,k,d]_q$ code over $GF(q)$ for given $q,k$ and $d$. A lower bound on $n_q(k,d)$ has been provided by the well known Griesmer bound. The purpose of this paper is to determine $n_q(5,d)$ for $$q^4-q^3-q -\sqrt q-2 B.K.Dass (Delhi)