论文标题
z_ {p^s}之间的等价性
Equivalences among Z_{p^s}-linear Generalized Hadamard Codes
论文作者
论文摘要
$ \ z_ {p^s} $ - 长度$ n $的添加代码是$ \ z_ {p^s}^n $的子组，可以看作是$ \ z_2 $，$ \ z__4 $或$ \ z__ {2^s} $的线性代码的概括。 $ \ z_ {p^s} $ - 线性概括性hadamard（gh）代码是$ \ z_p $上的GH代码，它是$ \ z_ {p^s} $的图像，通过广义灰色地图。通过使用内核的维度对这些代码进行部分分类。在本文中，我们确定某些$ \ z_ {p^s} $ - 一旦修复了$ t $，$ p^t $的长度$ p^t $是等效的。这使我们可以改善此类非级代码数量的已知上限。此外，最多$ t = 10 $，这个新的上限与已知的下限（基于内核的等级和维度）相吻合。
The $\Z_{p^s}$-additive codes of length $n$ are subgroups of $\Z_{p^s}^n$, and can be seen as a generalization of linear codes over $\Z_2$, $\Z_4$, or $\Z_{2^s}$ in general. A $\Z_{p^s}$-linear generalized Hadamard (GH) code is a GH code over $\Z_p$ which is the image of a $\Z_{p^s}$-additive code by a generalized Gray map. A partial classification of these codes by using the dimension of the kernel is known. In this paper, we establish that some $\Z_{p^s}$-linear GH codes of length $p^t$ are equivalent, once $t$ is fixed. This allows us to improve the known upper bounds for the number of such nonequivalent codes. Moreover, up to $t=10$, this new upper bound coincides with a known lower bound (based on the rank and dimension of the kernel).
