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In this paper, we investigate self-dual double circulant, and self-dual and linear complementary dual (LCD) double negacirculant codes over a finite ring  R  = F  q   +  u F  q   +  v F  q   +  uv F  q  , where  u  2  =  u ,  v  2  =  v ,  uv  =  vu  and  q  =  p m  . We study the algebraic structure of double circulant codes over  R . 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  R . We compute distance bounds for self-dual double circulant codes over  R . 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  R .

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Self-dual double circulant, self-dual double negacirculant and LCD double negacirculant codes over the ring F  q  [ u,v ]/&#x27E8; u  2 - u ,  v  2 - v ,  uv-vu &#x27E9;