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On the Minimum Length of q-ary Linear Codes of Dimension Five
Authors:TATSUYA MARUTA
Affiliation:(1) Aichi Prefectural Women's Junior College, Mizuho, 467 Nagoya, Japan
Abstract:Let 
$$n_q left( {k,d} right) $$
be the smallest integer n for which there exists a linear code of length n, dimension k and minimum Hamming distance d over the Galois field GF(q). In this paper we determine 
$$n_q left( {5,d} right) $$
for 
$$q^4 - q^3 - q - sqrt q - 2 < d leqslant q^4 - q^3 + q^2 - q$$
for all q, using a geometric method.
Keywords:linear code  the Griesmer bound  minihyper.
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