On complementary dual multinegacirculant codes
Alahmadi, Adel and Güneri, Cem and Özkaya, Buket and Shoaib, Hatoon and Sole, Patrick (2020) On complementary dual multinegacirculant codes. Cryptography and Communications, 12 (1). pp. 101-113. ISSN 1936-2447 (Print) 1936-2455 (Online)
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Official URL: http://dx.doi.org/10.1007/s12095-019-00364-8
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 innite families of LCD multinegacirculant codes with relative distance satisfying a modied Varshamov-Gilbert bound.
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