Ternary LCD codes and their connection to bent functions

Linear Complementary Dual (LCD) codes over finite fields possess remarkable correlation and orthogonality properties, which render them highly effective in defending against side-channel attacks. This paper delves into the properties of LCD codes and their connections to quadratic forms associated with linear codes and Bent functions. We demonstrate that a code $ \mathcal{C} $ is an LCD code if and only if the quadratic form $ \left.Q\right|_{\mathcal{C}} $ associated with $ \mathcal{C} $ is a Bent function. Furthermore, by leveraging the theory of quadratic forms, we derive key results, including conditions for determining ternary LCD codes based on their weight distributions.