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Some properties of dihedral group codes
May 17, 2020 Β· Declared Dead Β· π arXiv.org
"No code URL or promise found in abstract"
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Authors
Kirill V. Vedenev, Vladimir M. Deundyak
arXiv ID
2005.08283
Category
math.RA
Cross-listed
cs.IT
Citations
0
Venue
arXiv.org
Last Checked
3 months ago
Abstract
In this paper, we study the dihedral codes, i.e. the left ideals of $\mathbb{F}_qD_{n}$ in the case $\gcd(q, n) = 1$. An explicit algebraic description of the dihedral codes and their duals is obtained. In addition, a criterion for self-duality of a dihedral code is obtained. Bases, generating and check matrices of dihedral codes are constructed. Given a dihedral code, we consider exterior and interior codes that are induced by cyclic codes. Using this codes, some properties of generating matrices are described and a connection to cyclic code theory is established. In addition, some estimates of code parameters are obtained and several illustrative examples are given.
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