On self-dual, LCD double circulant and double negacirculant codes

Let [Formula: see text] be an odd prime, [Formula: see text] and we consider a finite non-chain ring [Formula: see text], with [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text]. This work focuses on self-dual, linear complementary dual (LCD) double circulant, and double negacirculant codes over [Formula: see text]. We derive the necessary and sufficient conditions for a double circulant code to be a self-dual and an Euclidean LCD code over [Formula: see text]. We also discuss similar results for the double negacirculant code. Moreover, we establish a formula for counting the number of LCD and self-dual double circulant and double negacirculant codes over [Formula: see text]. Furthermore, we establish distance bounds for double circulant codes over [Formula: see text] and demonstrate the asymptotic properties of families of LCD and self-dual double circulant codes by using a Gray map.