On linear complementary-dual multinegacirculant codes

Linear codes with complementary-duals (LCD) are linear codes that intersect with their dual trivially. Multinegacirculant codes of index $2$ that are LCD are characterized algebraically and some good codes are found in this family. Exact enumeration is performed for indices 2 and 3, and for all indices $t$ for a special case of the co-index by using their concatenated structure. Asymptotic existence results are derived for the special class of such codes that are one-generator and have co-index a power of two by means of Dickson polynomials. This shows that there are infinite families of LCD multinegacirculant codes with relative distance satisfying a modified Varshamov-Gilbert bound.