Year 2020, Volume 7 , Issue 1, Pages 55 - 71 2020-02-29

$G$-codes over formal power series rings and finite chain rings

Steven T. DOUGHERTY [1] , Joe GİLDEA [2] , Adrian KORBAN [3]


In this work, we define $G$-codes over the infinite ring $R_\infty$ as ideals in the group ring $R_\infty G$. We show that the dual of a $G$-code is again a $G$-code in this setting. We study the projections and lifts of $G$-codes over the finite chain rings and over the formal power series rings respectively. We extend known results of constructing $\gamma$-adic codes over $R_\infty$ to $\gamma$-adic $G$-codes over the same ring. We also study $G$-codes over principal ideal rings.
$G$-codes, Finite chain rings, Formal power series rings, $\gamma$-adic codes
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Primary Language en
Subjects Engineering
Journal Section Articles
Authors

Orcid: 0000-0003-4877-1923
Author: Steven T. DOUGHERTY

Orcid: 0000-0001-7242-779X
Author: Joe GİLDEA

Orcid: 0000-0001-5206-6480
Author: Adrian KORBAN (Primary Author)

Dates

Publication Date : February 29, 2020

Bibtex @research article { jacodesmath645026, journal = {Journal of Algebra Combinatorics Discrete Structures and Applications}, issn = {}, eissn = {2148-838X}, address = {}, publisher = {Yildiz Technical University}, year = {2020}, volume = {7}, pages = {55 - 71}, doi = {10.13069/jacodesmath.645026}, title = {\$G\$-codes over formal power series rings and finite chain rings}, key = {cite}, author = {Dougherty, Steven T. and Gi̇ldea, Joe and Korban, Adrian} }
APA Dougherty, S , Gi̇ldea, J , Korban, A . (2020). $G$-codes over formal power series rings and finite chain rings . Journal of Algebra Combinatorics Discrete Structures and Applications , 7 (1) , 55-71 . DOI: 10.13069/jacodesmath.645026
MLA Dougherty, S , Gi̇ldea, J , Korban, A . "$G$-codes over formal power series rings and finite chain rings" . Journal of Algebra Combinatorics Discrete Structures and Applications 7 (2020 ): 55-71 <https://dergipark.org.tr/en/pub/jacodesmath/issue/51990/645026>
Chicago Dougherty, S , Gi̇ldea, J , Korban, A . "$G$-codes over formal power series rings and finite chain rings". Journal of Algebra Combinatorics Discrete Structures and Applications 7 (2020 ): 55-71
RIS TY - JOUR T1 - $G$-codes over formal power series rings and finite chain rings AU - Steven T. Dougherty , Joe Gi̇ldea , Adrian Korban Y1 - 2020 PY - 2020 N1 - doi: 10.13069/jacodesmath.645026 DO - 10.13069/jacodesmath.645026 T2 - Journal of Algebra Combinatorics Discrete Structures and Applications JF - Journal JO - JOR SP - 55 EP - 71 VL - 7 IS - 1 SN - -2148-838X M3 - doi: 10.13069/jacodesmath.645026 UR - https://doi.org/10.13069/jacodesmath.645026 Y2 - 2019 ER -
EndNote %0 Journal of Algebra Combinatorics Discrete Structures and Applications $G$-codes over formal power series rings and finite chain rings %A Steven T. Dougherty , Joe Gi̇ldea , Adrian Korban %T $G$-codes over formal power series rings and finite chain rings %D 2020 %J Journal of Algebra Combinatorics Discrete Structures and Applications %P -2148-838X %V 7 %N 1 %R doi: 10.13069/jacodesmath.645026 %U 10.13069/jacodesmath.645026
ISNAD Dougherty, Steven T. , Gi̇ldea, Joe , Korban, Adrian . "$G$-codes over formal power series rings and finite chain rings". Journal of Algebra Combinatorics Discrete Structures and Applications 7 / 1 (February 2020): 55-71 . https://doi.org/10.13069/jacodesmath.645026
AMA Dougherty S , Gi̇ldea J , Korban A . $G$-codes over formal power series rings and finite chain rings. Journal of Algebra Combinatorics Discrete Structures and Applications. 2020; 7(1): 55-71.
Vancouver Dougherty S , Gi̇ldea J , Korban A . $G$-codes over formal power series rings and finite chain rings. Journal of Algebra Combinatorics Discrete Structures and Applications. 2020; 7(1): 55-71.