论文标题
部分可观测时空混沌系统的无模型预测
Intersections of linear codes and related MDS codes with new Galois hulls
论文作者
论文摘要
令$ \ mathrm {slaut}（\ mathbb {f} _ {q}^{n}）$表示$ \ mathbb {f} _ {q} _ {q}^{n}^{n} $的所有半线性异构体的组，wher在本文中，我们研究了与$σ$ duals相关的线性代码的一般属性，以$σ\ in \ mathrm {slaut}（\ mathbb {f} _ {q} _ {q}^{n}）$。我们表明，可以通过此类代码的发电机矩阵及其$σ$ duals确定两个线性代码的相交的尺寸。我们还表明，线性代码的$σ$船体的尺寸可以由IT的发电机矩阵或其$σ$ dual确定。我们对矩阵产品代码的$σ$双重和$σ$船体进行表征。我们还研究了一对矩阵 - 产品代码的交集。我们提供了必要且充分的条件，在该条件下，其$σ$ dual中包含的通用芦苇 - 固体（GRS）代码或扩展GRS代码的任何代码字。作为一个应用程序，我们构建了11个家庭，拥有$ Q $ -ARY MDS代码的新$ \ ell $ -Galois Hulls，满足$ 2（e- \ ell）\ Mid E $，而Cao的最新论文（IEEETrans。Inf。Inf。47（12），7964-7984，2021）和FANG and FANG等。 （Cryptogr。Commun。14（1），145-159，2022）当$ \ ell \ neq \ frac {e} {2} $时。
Let $\mathrm{SLAut}(\mathbb{F}_{q}^{n})$ denote the group of all semilinear isometries on $\mathbb{F}_{q}^{n}$, where $q=p^{e}$ is a prime power. In this paper, we investigate general properties of linear codes associated with $σ$ duals for $σ\in\mathrm{SLAut}(\mathbb{F}_{q}^{n})$. We show that the dimension of the intersection of two linear codes can be determined by generator matrices of such codes and their $σ$ duals. We also show that the dimension of $σ$ hull of a linear code can be determined by a generator matrix of it or its $σ$ dual. We give a characterization on $σ$ dual and $σ$ hull of a matrix-product code. We also investigate the intersection of a pair of matrix-product codes. We provide a necessary and sufficient condition under which any codeword of a generalized Reed-Solomon (GRS) code or an extended GRS code is contained in its $σ$ dual. As an application, we construct eleven families of $q$-ary MDS codes with new $\ell$-Galois hulls satisfying $2(e-\ell)\mid e$, which are not covered by the latest papers by Cao (IEEE Trans. Inf. Theory 67(12), 7964-7984, 2021) and by Fang et al. (Cryptogr. Commun. 14(1), 145-159, 2022) when $\ell\neq \frac{e}{2}$.
