On optimal linear codes of dimension 4
In coding theory, the problem of finding the shortest linear codes for a fixed set of parameters is central. Given the dimension $k$, the minimum weight $d$, and the order $q$ of the finite field $\bF_q$ over which the code is defined, the function $n_q(k, d)$ specifies the smallest length $n$ for...
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Yildiz Technical University
2021-05-01
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| Series: | Journal of Algebra Combinatorics Discrete Structures and Applications |
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| Online Access: | https://jacodesmath.com/index.php/jacodesmath/article/view/119 |
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doaj-1d0104c431354d7d8145c525d852a57a2021-07-17T20:19:35ZengYildiz Technical UniversityJournal of Algebra Combinatorics Discrete Structures and Applications2148-838X2021-05-0181108On optimal linear codes of dimension 4Nanami BonoMaya FujiiTatsuya Maruta0Osaka Prefecture University In coding theory, the problem of finding the shortest linear codes for a fixed set of parameters is central. Given the dimension $k$, the minimum weight $d$, and the order $q$ of the finite field $\bF_q$ over which the code is defined, the function $n_q(k, d)$ specifies the smallest length $n$ for which an $[n, k, d]_q$ code exists. The problem of determining the values of this function is known as the problem of optimal linear codes. Using the geometric methods through projective geometry, we determine $n_q(4,d)$ for some values of $d$ by constructing new codes and by proving the nonexistence of linear codes with certain parameters. https://jacodesmath.com/index.php/jacodesmath/article/view/119Optimal linear codes,Griesmer bound,Geometric method |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Nanami Bono Maya Fujii Tatsuya Maruta |
| spellingShingle |
Nanami Bono Maya Fujii Tatsuya Maruta On optimal linear codes of dimension 4 Journal of Algebra Combinatorics Discrete Structures and Applications Optimal linear codes,Griesmer bound,Geometric method |
| author_facet |
Nanami Bono Maya Fujii Tatsuya Maruta |
| author_sort |
Nanami Bono |
| title |
On optimal linear codes of dimension 4 |
| title_short |
On optimal linear codes of dimension 4 |
| title_full |
On optimal linear codes of dimension 4 |
| title_fullStr |
On optimal linear codes of dimension 4 |
| title_full_unstemmed |
On optimal linear codes of dimension 4 |
| title_sort |
on optimal linear codes of dimension 4 |
| publisher |
Yildiz Technical University |
| series |
Journal of Algebra Combinatorics Discrete Structures and Applications |
| issn |
2148-838X |
| publishDate |
2021-05-01 |
| description |
In coding theory, the problem of finding the shortest linear codes for a fixed set of parameters is central. Given the dimension $k$, the minimum weight $d$, and the order $q$ of the finite field $\bF_q$ over which the code is defined, the function $n_q(k, d)$ specifies the smallest length $n$ for which an $[n, k, d]_q$ code exists. The problem of determining the values of this function is known as the problem of optimal linear codes. Using the geometric methods through projective geometry, we determine $n_q(4,d)$ for some values of $d$ by constructing new codes and by proving the nonexistence of linear codes with certain parameters.
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| topic |
Optimal linear codes,Griesmer bound,Geometric method |
| url |
https://jacodesmath.com/index.php/jacodesmath/article/view/119 |
| work_keys_str_mv |
AT nanamibono onoptimallinearcodesofdimension4 AT mayafujii onoptimallinearcodesofdimension4 AT tatsuyamaruta onoptimallinearcodesofdimension4 |
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1721296530096259072 |