Paper Info
Title
LCD and Self-Orthogonal Group Codes in a Finite Abelian $p$ -Group Algebra
Abstract
Let <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Bbb F_{q}$ </tex-math></inline-formula> be a finite field with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula> elements and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> be a prime with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\gcd (p,q)=1$ </tex-math></inline-formula> . Let <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$G$ </tex-math></inline-formula> be a finite abelian <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> -group and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Bbb F_{q}(G)$ </tex-math></inline-formula> be a group algebra. In this paper, we find all primitive idempotents and minimal abelian group codes in the group algebra <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Bbb F_{q}(G)$ </tex-math></inline-formula> . Furthermore, we give all LCD abelian codes (linear code with complementary dual) and self-orthogonal abelian codes of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Bbb F_{q}(G)$ </tex-math></inline-formula> .
Year
DOI
Venue
2020
10.1109/TIT.2019.2923758
IEEE Transactions on Information Theory
Keywords
DocType
Volume
Liquid crystal displays,Algebra,Linear codes,Cryptography,Hamming distance,Indexes
Journal
66
Issue
ISSN
Citations 
5
0018-9448
0
PageRank 
References 
Authors
0.34
0
3
Name
Order
Citations
PageRank
Fengwei Li110513.73
Qin Yue219221.13
Yansheng Wu31510.07