Additive codes have attracted considerable attention for their potential to outperform linear codes. However, distinguishing strictly additive codes from those that are equivalent to linear codes remains a fundamental challenge. To resolve this ambiguity, we introduce a deterministic test that requires only the generator matrix of the code. We apply this test to verify the strict additivity of several quaternary additive codes recently reported in the literature. Conversely, we demonstrate that a previously known additive complementary dual (ACD) code is equivalent to a linear Hermitian LCD code, thereby improving the best-known bounds for such linear codes.

翻译：加法码因其性能可能超越线性码而受到广泛关注。然而，严格区分加法码与等价于线性码的加法码仍是一个根本性挑战。为消除这一模糊性，我们提出一种仅需码的生成矩阵的确定性判定方法。应用此方法，我们验证了近期文献中报道的若干四元加法码的严格加法性。反之，我们证明了一种先前已知的加法互补对偶码等价于线性Hermitian LCD码，从而改进了此类线性码的最佳已知界。