LCD Codes and Self-orthogonal Codes in Finite Dihedral Group Algebras
Yanyan Gao , Qin Yue , Yansheng Wu
Chinese Annals of Mathematics, Series B ›› 2021, Vol. 42 ›› Issue (5) : 791 -800.
LCD Codes and Self-orthogonal Codes in Finite Dihedral Group Algebras
Let ${\mathbb{F}_q}$ be a finite field with order q and D 2n be the dihedral group with 2n elements, and gcd(q, 2n) = 1. In this article, the authors give precise descriptions and enumerations of linear complementary dual (LCD) codes and self-orthogonal codes in the finite dihedral group algebras ${\mathbb{F}_q}[{D_{2n}}]$. Some numerical examples are also presented to illustrate the main results.
Group algebra / Dihedral group / LCD codes / Self-orthogonal codes
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| [3] |
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| [4] |
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| [5] |
|
| [6] |
Choosuwan, P., Jitman, S. and Udomkavanich, P., Self-abelian codes in some nonprincipal ideal group algebras, Math. Probl. Eng., Article ID: 9020173, 12 pages, 2016. |
| [7] |
|
| [8] |
|
| [9] |
|
| [10] |
|
| [11] |
|
| [12] |
|
| [13] |
|
| [14] |
|
| [15] |
|
| [16] |
|
| [17] |
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| [18] |
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