Self-dual double circulant, self-dual double negacirculant and LCD double negacirculant codes over the ring F[]/⟨2-, 2-, ⟩

Abstract

In this paper, we investigate self-dual double circulant, and self-dual and linear complementary dual (LCD) double negacirculant codes over a finite ring = F + F + F + F, where 2 = , 2 = , = and = . We study the algebraic structure of double circulant codes over . We provide necessary and sufficient conditions for a double circulant code to be a self-dual code. We give a formula to get the total number of self-dual double circulant codes over the ring . We compute distance bounds for self-dual double circulant codes over . In addition, by using a Gray map, we show that the families of self-dual double circulant codes under the Gray map are asymptotically good. Moreover, the algebraic structure of double negacirculant codes and necessary and sufficient conditions for a double negacirculant code to be a self-dual code and to be an LCD code are also given.We determine the total number of self-dual and LCD double negacirculant codes over