Geodesic
On optimal linear codes over \(\mathbb F_8\)
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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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.
DOI : 10.37236/521
Classification : 94B05, 94B27, 51E20, 05B25
Mots-clés : optimal linear codes 
@article{10_37236_521,
     author = {Rie Kanazawa and Tatsuya Maruta},
     title = {On optimal linear codes over \(\mathbb {F_8\)}},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/521},
     zbl = {1221.94081},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/521/}
}
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Rie Kanazawa; Tatsuya Maruta. On optimal linear codes over \(\mathbb F_8\). The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/521

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