On complementary dual multinegacirculant codes

• DOI: 10.1007/s12095-019-00364-8
• Publication Date: 2019-06-21T08:02:46Z
• Authors: Adel Alahmadi; Cem Güneri; Buket Özkaya; Hatoon Shoaib; Patrick Solé
• Keywords: Dual polyhedron; Enumeration

Linear codes with complementary duals intersect with their duals trivially. Multinegacirculant codes that are complementary dual are characterized algebraically and some good codes are found in this family. Exact enumeration is performed for indices 2 and 3, whereas special choices of the co-index and base field size are needed for higher indices. Asymptotic existence results are derived for the special class of such codes that have co-index a power of two by means of Dickson polynomials. This shows that there are infinite families of complementary dual multinegacirculant codes with relative distance satisfying a modified Gilbert-Varshamov bound.