  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.
