Year 2018, Volume 5 , Issue 1, Pages 5 - 18 2018-01-15

Hermitian self-dual quasi-abelian codes

Herbert S. PALİNES [1] , Somphong JİTMAN [2] , Romar B. Dela CRUZ [3]


Quasi-abelian codes constitute an important class of linear codes containing theoretically and practically interesting codes such as quasi-cyclic codes, abelian codes, and cyclic codes. In particular, the sub-class consisting of 1-generator quasi-abelian codes contains large families of good codes. Based on the well-known decomposition of quasi-abelian codes, the characterization and enumeration of Hermitian self-dual quasi-abelian codes are given. In the case of 1-generator quasi-abelian codes, we offer necessary and sufficient conditions for such codes to be Hermitian self-dual and give a formula for the number of these codes. In the case where the underlying groups are some $p$-groups, the actual number of resulting Hermitian self-dual quasi-abelian codes are determined.
Hermitian self-dual codes, Quasi-abelian codes, 1-generator, p-groups
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Subjects Engineering
Journal Section Articles
Authors

Author: Herbert S. PALİNES

Orcid: 0000-0003-1076-0866
Author: Somphong JİTMAN

Author: Romar B. Dela CRUZ

Dates

Publication Date : January 15, 2018

Bibtex @research article { jacodesmath327399, journal = {Journal of Algebra Combinatorics Discrete Structures and Applications}, issn = {}, eissn = {2148-838X}, address = {}, publisher = {Yildiz Technical University}, year = {2018}, volume = {5}, pages = {5 - 18}, doi = {10.13069/jacodesmath.327399}, title = {Hermitian self-dual quasi-abelian codes}, key = {cite}, author = {Pali̇nes, Herbert S. and Ji̇tman, Somphong and Cruz, Romar B. Dela} }
APA Pali̇nes, H , Ji̇tman, S , Cruz, R . (2018). Hermitian self-dual quasi-abelian codes . Journal of Algebra Combinatorics Discrete Structures and Applications , 5 (1) , 5-18 . DOI: 10.13069/jacodesmath.327399
MLA Pali̇nes, H , Ji̇tman, S , Cruz, R . "Hermitian self-dual quasi-abelian codes" . Journal of Algebra Combinatorics Discrete Structures and Applications 5 (2018 ): 5-18 <https://dergipark.org.tr/en/pub/jacodesmath/issue/33304/327399>
Chicago Pali̇nes, H , Ji̇tman, S , Cruz, R . "Hermitian self-dual quasi-abelian codes". Journal of Algebra Combinatorics Discrete Structures and Applications 5 (2018 ): 5-18
RIS TY - JOUR T1 - Hermitian self-dual quasi-abelian codes AU - Herbert S. Pali̇nes , Somphong Ji̇tman , Romar B. Dela Cruz Y1 - 2018 PY - 2018 N1 - doi: 10.13069/jacodesmath.327399 DO - 10.13069/jacodesmath.327399 T2 - Journal of Algebra Combinatorics Discrete Structures and Applications JF - Journal JO - JOR SP - 5 EP - 18 VL - 5 IS - 1 SN - -2148-838X M3 - doi: 10.13069/jacodesmath.327399 UR - https://doi.org/10.13069/jacodesmath.327399 Y2 - 2017 ER -
EndNote %0 Journal of Algebra Combinatorics Discrete Structures and Applications Hermitian self-dual quasi-abelian codes %A Herbert S. Pali̇nes , Somphong Ji̇tman , Romar B. Dela Cruz %T Hermitian self-dual quasi-abelian codes %D 2018 %J Journal of Algebra Combinatorics Discrete Structures and Applications %P -2148-838X %V 5 %N 1 %R doi: 10.13069/jacodesmath.327399 %U 10.13069/jacodesmath.327399
ISNAD Pali̇nes, Herbert S. , Ji̇tman, Somphong , Cruz, Romar B. Dela . "Hermitian self-dual quasi-abelian codes". Journal of Algebra Combinatorics Discrete Structures and Applications 5 / 1 (January 2018): 5-18 . https://doi.org/10.13069/jacodesmath.327399
AMA Pali̇nes H , Ji̇tman S , Cruz R . Hermitian self-dual quasi-abelian codes. Journal of Algebra Combinatorics Discrete Structures and Applications. 2018; 5(1): 5-18.
Vancouver Pali̇nes H , Ji̇tman S , Cruz R . Hermitian self-dual quasi-abelian codes. Journal of Algebra Combinatorics Discrete Structures and Applications. 2018; 5(1): 5-18.