Year 2019, Volume 6, Issue 1, Pages 13 - 20 2019-01-19

New Linear Codes over $GF(3)$, $GF(11)$, and $GF(13)$

Nuh Aydin [1] , Derek Foret [2]

37 149

Explicit construction of linear codes with best possible parameters is one of the major and challenging problems in coding theory. Cyclic codes and their various generalizations, such as quasi-twisted (QT) codes, are known to contain many codes with best known parameters. Despite the fact that these classes of codes have been extensively searched, we have been able to refine existing search algorithms to discover many new linear codes over the alphabets $\mathbb{F}_{3}$, $\mathbb{F}_{11}$, and $\mathbb{F}_{13}$ with better parameters. A total of 38 new linear codes over the three alphabets are presented.
Best known codes, Constacyclic codes, Quasi-cyclic codes, Quasi-twisted codes
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Primary Language en
Subjects Engineering
Journal Section Articles
Authors

Orcid: 0000-0002-5618-2427
Author: Nuh Aydin (Primary Author)

Author: Derek Foret

Dates

Publication Date: January 19, 2019

Bibtex @research article { jacodesmath508968, journal = {Journal of Algebra Combinatorics Discrete Structures and Applications}, issn = {}, eissn = {2148-838X}, address = {Yildiz Technical University}, year = {2019}, volume = {6}, pages = {13 - 20}, doi = {10.13069/jacodesmath.508968}, title = {New Linear Codes over \$GF(3)\$, \$GF(11)\$, and \$GF(13)\$}, key = {cite}, author = {Aydin, Nuh and Foret, Derek} }
APA Aydin, N , Foret, D . (2019). New Linear Codes over $GF(3)$, $GF(11)$, and $GF(13)$. Journal of Algebra Combinatorics Discrete Structures and Applications, 6 (1), 13-20. DOI: 10.13069/jacodesmath.508968
MLA Aydin, N , Foret, D . "New Linear Codes over $GF(3)$, $GF(11)$, and $GF(13)$". Journal of Algebra Combinatorics Discrete Structures and Applications 6 (2019): 13-20 <http://dergipark.org.tr/jacodesmath/issue/42703/508968>
Chicago Aydin, N , Foret, D . "New Linear Codes over $GF(3)$, $GF(11)$, and $GF(13)$". Journal of Algebra Combinatorics Discrete Structures and Applications 6 (2019): 13-20
RIS TY - JOUR T1 - New Linear Codes over $GF(3)$, $GF(11)$, and $GF(13)$ AU - Nuh Aydin , Derek Foret Y1 - 2019 PY - 2019 N1 - doi: 10.13069/jacodesmath.508968 DO - 10.13069/jacodesmath.508968 T2 - Journal of Algebra Combinatorics Discrete Structures and Applications JF - Journal JO - JOR SP - 13 EP - 20 VL - 6 IS - 1 SN - -2148-838X M3 - doi: 10.13069/jacodesmath.508968 UR - https://doi.org/10.13069/jacodesmath.508968 Y2 - 2018 ER -
EndNote %0 Journal of Algebra Combinatorics Discrete Structures and Applications New Linear Codes over $GF(3)$, $GF(11)$, and $GF(13)$ %A Nuh Aydin , Derek Foret %T New Linear Codes over $GF(3)$, $GF(11)$, and $GF(13)$ %D 2019 %J Journal of Algebra Combinatorics Discrete Structures and Applications %P -2148-838X %V 6 %N 1 %R doi: 10.13069/jacodesmath.508968 %U 10.13069/jacodesmath.508968
ISNAD Aydin, Nuh , Foret, Derek . "New Linear Codes over $GF(3)$, $GF(11)$, and $GF(13)$". Journal of Algebra Combinatorics Discrete Structures and Applications 6 / 1 (January 2019): 13-20. https://doi.org/10.13069/jacodesmath.508968
AMA Aydin N , Foret D . New Linear Codes over $GF(3)$, $GF(11)$, and $GF(13)$. Journal of Algebra Combinatorics Discrete Structures and Applications. 2019; 6(1): 13-20.
Vancouver Aydin N , Foret D . New Linear Codes over $GF(3)$, $GF(11)$, and $GF(13)$. Journal of Algebra Combinatorics Discrete Structures and Applications. 2019; 6(1): 20-13.