Double circulant self-dual and LCD codes over Galois rings

This paper investigates the existence, enumeration and asymptotic performance of self-dual and LCD double circulant codes over Galois rings of characteristic p and order p with p and odd prime. When p ≡ 3 (mod 4), we give an algorithm to construct a duality preserving bijective Gray map from such a Galois ring to Z p2 . Using random coding, we obtain families of asymptotically good self-dual and LCD codes over Zp2, for the metric induced by the standard Fp-valued Gray maps.