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Double circulant self-dual and LCD codes over Galois rings
- Publication Year :
- 2018
-
Abstract
- This paper investigates the existence, enumeration and asymptotic performance of self-dual and LCD double circulant codes over Galois rings of characteristic $p^2$ and order $p^4$ with $p$ and odd prime. When $p \equiv 3 \pmod{4},$ we give an algorithm to construct a duality preserving bijective Gray map from such a Galois ring to $\mathbb{Z}_{p^2}^2.$ Using random coding, we obtain families of asymptotically good self-dual and LCD codes over $\mathbb{Z}_{p^2},$ for the metric induced by the standard $\mathbb{F}_p$-valued Gray maps.<br />Comment: Sbumitted on 4, December, 20 pages
- Subjects :
- Computer Science - Information Theory
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1801.06624
- Document Type :
- Working Paper