Double circulant self-dual and LCD codes over Galois rings

01/20/2018

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by   Minjia Shi, et al.

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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 ≡ 3 4, we give an algorithm to construct a duality preserving bijective Gray map from such a Galois ring to Z_p^2^2. Using random coding, we obtain families of asymptotically good self-dual and LCD codes over Z_p^2, for the metric induced by the standard F_p-valued Gray maps.