ON THE MINIMUM LENGTH OF SOME LINEAR CODES OF DIMENSION 6
Eun Ju Cheon, Takao Kato · Bulletin of the Korean Mathematical Society · 2008
For $q^5-q^3-q^2-q+1{\leq}d{\leq}q^5-q^3-q^2$ , we prove the non-existence of a $[g_q(6,d),6,d]_q$ code and we give a $[g_q(6,d)+1,6,d]_q$ code by constructing appropriate 0-cycle in the projective space, where $g_q (k,d)={{\sum}^{k-1}_{i=0}}{\lceil}\frac{d}{q^i}{\rceil}$ . Consequently, we have the minimum length $n_q(6,d)=g_q(6,d)+1\;for\;q^5-q^3-q^2-q+1{\leq}d{\leq}q^5-q^3-q^2\;and\;q{\geq}3$ .