Let \(\mathbb {F}_q\) denote the finite field of order q, and let \(\Lambda =(\lambda _1,\lambda _2,\cdots ,\lambda _\ell ),\) where \(\lambda _1,\lambda _2,\cdots ,\lambda _\ell \) are non-zero elements of \(\mathbb {F}_q.\) Let \(n =m_1+m_2+\cdots +m_\ell ,\) where \(m_1,m_2,\cdots ,m_\ell \) are arbitrary positive integers (not necessarily coprime to q). In this paper, we study algebraic structures of \(\Lambda \)-multi-twisted (\(\Lambda \)-MT) codes of length n and block lengths \((m_1,m_2,\cdots ,m_{\ell })\) over \(\mathbb {F}_q\) and their Galois duals (i.e., their orthogonal complements with respect to the Galois inner product on \(\mathbb {F}_{q}^n\)). We develop generator theory for \(\Lambda \)-MT codes of length n over \(\mathbb {F}_{q}\) and show that each \(\Lambda \)-MT code of length n over \(\mathbb {F}_{q}\) has a unique nice normalized generating set. With the help of a normalized generating set, we explicitly determine the dimension and a generating set of the Galois dual of each \(\Lambda \)-MT code of length n over \(\mathbb {F}_{q}.\) We also provide a trace description of all \(\Lambda \)-MT codes of length n over \(\mathbb {F}_{q}\) by using the generalized discrete Fourier transform (GDFT), which gives rise to a method to construct these codes. We further provide necessary and sufficient conditions under which a Euclidean self-dual \(\Lambda \)-MT code of length n over \(\mathbb {F}_{2^e}\) is a Type II code when \(\lambda _i=1\) and \(m_i = n_i2^a\) for \( 1\le i \le \ell ,\) where \(a \ge 0\) is an integer and \(n_1, n_2, \cdots , n_{\ell }\) are odd positive integers satisfying \(n_1 \equiv n_2 \equiv \cdots \equiv n_{\ell }~ (\text {mod }4).\) Besides this, we obtain several linear codes with best-known and optimal parameters from 1-generator \(\Lambda \)-MT codes over \(\mathbb {F}_{q},\) where \(2 \le q \le 7.\) It is worth mentioning that these code parameters can not be attained by any of their subclasses (such as constacyclic and quasi-twisted codes) containing record breaker codes.

让\（\ mathbb {F} _q \）表示顺序的有限域q，并让\（\ LAMBDA =（\拉姆达_1，\拉姆达_2，\ cdots，\拉姆达_ \ ELL），\）其中\（ \lambda_1,\lambda_2,\cdots,\lambda_\ell\)是\(\mathbb {F}_q.\)的非零元素让\(n =m_1+m_2+\cdots +m_\ell , \)其中\(m_1,m_2,\cdots ,m_\ell \)是任意正整数（不一定与q互质）。在本文中，我们研究了\(\Lambda \) -multi-twisted ( \(\Lambda \) -MT) 长度为n和块长度\((m_1,m_2,\cdots ,m_{\ell })\)结束\(\mathbb {F}_q\)和它们的伽罗瓦对偶（即它们关于\(\mathbb {F}_{q}^n\)上的伽罗瓦内积的正交补集）。我们开发发生器理论\（\ LAMBDA \） -MT长度的码Ñ超过\（\ mathbb {F} _ {Q} \） ，并显示每个\（\ LAMBDA \） -MT长度的代码Ñ超过\（ \mathbb {F}_{q}\)有一个独特的好的归一化生成集。用的归一化发电机组的帮助下，我们明确地确定尺寸和每个所述伽罗瓦双重的发电机组\（\ LAMBDA \） -MT长度的代码Ñ超过\（\ mathbb {F} _ {Q}。\ )我们还通过使用广义离散傅立叶变换 (GDFT)提供了所有长度为n 的\(\Lambda \) -MT 代码在\(\mathbb {F}_{q}\) 上的轨迹描述，这产生了构造这些代码的方法。我们进一步提供了充分必要条件，在该条件下，长度为n超过\(\mathbb {F}_{2^e}\)的欧几里得自对偶\(\Lambda \) -MT 代码是类型 II 代码，当\( \lambda _i=1\)和\(m_i = n_i2^a\)对于\( 1\le i \le \ell ,\)其中\(a \ge 0\)是一个整数，而\(n_1, n_2, \cdots , n_{\ell }\)是奇数正整数满足\(n_1 \equiv n_2 \equiv \cdots \equiv n_{\ell }~ (\text {mod }4).\)除此之外，我们从1-generator \( \Lambda \) -MT 代码超过\(\mathbb {F}_{q},\) where \(2 \le q \le 7.\)值得一提的是，这些代码参数无法通过任何它们的子类（例如恒环和准扭曲代码）包含破纪录的代码。