Inspired by the work of Zhou (Des Codes Cryptogr 88:841–850, 2020) based on the paper of Schmidt (J Algebraic Combin 42(2):635–670, 2015), we investigate the equivalence issue of maximum d-codes of Hermitian matrices. More precisely, in the space \({{H}}_n(q^2)\) of Hermitian matrices over \({\mathbb {F}}_{q^2}\) we have two possible equivalences: the classical one coming from the maps that preserve the rank in \({\mathbb {F}}_{q^2}^{n\times n}\), and the one that comes from restricting to those maps preserving both the rank and the space \({H}_n(q^2)\). We prove that when \(d<n\) and the codes considered are maximum additive d-codes and \((n-d)\)-designs, these two equivalence relations coincide. As a consequence, we get that the idealisers of such codes are not distinguishers, unlike what usually happens for rank metric codes. Finally, we deal with the combinatorial properties of known maximum Hermitian codes and, by means of this investigation, we present a new family of maximum Hermitian 2-code, extending the construction presented by Longobardi et al. (Discrete Math 343(7):111871, 2020).

受周（Des Codes Cryptogr 88：841–850，2020）的启发（基于Schmidt（J Algebraic Combin 42（2）：635–670，2015）的论文），我们研究了最大d码的等价问题埃尔米特矩阵。更准确地说，在\（{\ mathbb {F}} _ {q ^ 2} \）上Hermitian矩阵的空间\（{{H}} _ n（q ^ 2）\）中，我们有两个可能的等价关系：一张来自将地图保留在\（{{mathbb {F}} _ {q ^ 2} ^ {n \ times n} \）中的地图，另一张来自于将地图限制为同时保留排名和空间\（{H} _n（q ^ 2）\）。我们证明当\（d <n \）和所考虑的代码为最大加法d -codes和\（（nd）\）-设计，这两个等效关系重合。结果，我们得到了这样的代码的理想化者不是区分符，这与等级度量代码通常发生的情况不同。最后，我们处理已知的最大Hermitian码的组合性质，并通过此调查，我们提出了一个最大Hermitian 2码的新族，扩展了Longobardi等人的结构。（离散数学343（7）：111871，2020）。