On Additive Complementary Dual Codes over ℤ2RS and their MacWilliams identities

Abstract

In this paper, we study Additive Complementary Dual (ACD) codes over a mixed alphabet ℤ₂RS, where R = ℤ₂ + uℤ₂ and S = ℤ₂ + uℤ₂ + vℤ₂ + uvℤ₂, under the conditions u² = 0, v² = 0, and uv = vu. An additive code will prove to be an ACD code under certain conditions. In addition, it is a necessary and sufficient condition for a separable additive code to be an ACD code. Certain additive codes improve into binary linear complementary dual codes under a gray map that we investigate. Furthermore, a few types of weight enumerators are also calculated, and the associated MacWilliams identities are discussed with supportive examples.