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{\bf Rie Kanazawa and Tatsuya Maruta}
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{\bf On Optimal Linear Codes over ${\mathbb{F}}_8$}
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Let $n_q(k,d)$ be the smallest integer $n$ for which there exists an
$[n,k,d]_q$ code for given $q,k,d$. It is known that $n_8(4,d) =
\sum_{i=0}^{3} \left\lceil d/8^i \right\rceil$ for all $d \ge 833$.
As a continuation of Jones et al. [Electronic J. Combinatorics 13
(2006), \#R43], we determine $n_8(4,d)$ for 117 values of $d$ with
$113 \le d \le 832$ and give upper and lower bounds on $n_8(4,d)$ for
other $d$ using geometric methods and some extension theorems for
linear codes.



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