Emergent Mind
Double circulant self-dual and LCD codes over Galois rings
(1801.06624)
Published Jan 20, 2018
in
cs.IT
and
math.IT
Abstract
This paper investigates the existence, enumeration and asymptotic performance of self-dual and LCD double circulant codes over Galois rings of characteristic $p2$ and order $p4$ 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 $\mathbb{Z}{p2}2.$ Using random coding, we obtain families of asymptotically good self-dual and LCD codes over $\mathbb{Z}{p2},$ for the metric induced by the standard $\mathbb{F}_p$-valued Gray maps.
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