Geodesic
On the minimum length of linear codes over the field of 9 elements
Kazuki Kumegawa ; Ysukasa Okazaki ; Tatsuya Maruta1
1Osaka Prefecture University
The electronic journal of combinatorics, Tome 24 (2017) no. 1
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We construct a lot of new $[n,4,d]_9$ codes whose lengths are close to the Griesmer bound and prove the nonexistence of some linear codes attaining the Griesmer bound using some geometric techniques through projective geometries to determine the exact value of $n_9(4,d)$ or to improve the known bound on $n_9(4,d)$ for given values of $d$, where $n_q(k,d)$ is the minimum length $n$ for which an $[n,k,d]_q$ code exists. We also give the updated table for $n_9(4,d)$ for all $d$ except some known cases.
DOI : 10.37236/6394
Classification : 94B05, 94B65
Mots-clés : optimal linear codes, Griesmer bound, projective dual, geometric puncturing

Kazuki Kumegawa    ; Ysukasa Okazaki    ; Tatsuya Maruta  1

1 Osaka Prefecture University 
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     title = {On the minimum length of linear codes over the field of 9 elements},
     journal = {The electronic journal of combinatorics},
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Kazuki Kumegawa; Ysukasa Okazaki; Tatsuya Maruta. On the minimum length of linear codes over the field of 9 elements. The electronic journal of combinatorics, Tome 24 (2017) no. 1. doi: 10.37236/6394

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