论文标题
加权坐标Poset块代码
Weighted Coordinates Poset Block Codes
论文作者
论文摘要
给定$ [n] = \ {1,2，\ ldots，n \} $，$ [n] $上的部分顺序$ \ preceq $，标签映射$π：[n] \ rightarrow \ rightarrow \ mathbb {n} $ with $π（i）= k_i $ with $ \ sum sum um y sum unliend \ Mathbb {f} _ {q}^{k_1} \ oplus \ mathbb {f} _ {q}^{k_2} \ oplus \ ldots \ ldots \ ldots \ ldots \ oplus \ oplus \ oplus \ mathbb {f}函数$ w $ on $ \ mathbb {f} _q $，我们定义了poset块公制$ d _ {（p，p，w，w，π）} $上的$ \ m \ m \ mathbb {f} _ {q}^{q}^{n} $基于poset poset $ p =（n]，\ preceq）$。度量$ d _ {（p，w，π）} $被称为加权坐标poset块公制（$（p，w，π）$ - 公制）。它扩展了由L. Panek和J. A. Pinheiro引入的加权坐标POSET度量标准（$（p，w）$ - 公制），并概括了由M. M. M. M. S. Alves等人介绍的Poset Block Metric（$（P，π）$ - 公制）。我们确定$（p，w，π）$ - 空间的完整重量分布，从而以$（p，w）$ - space，$（p，π）$ - 空间，$π$ -space和$ p $ -p $ -space作为特殊情况。我们以$（p，w，π）$ - 代码和$（p，w）$ - 代码获得单例。特别是，我们重新攻击了有关$（p，π）$ - 公制和$ p $ - metric的任何代码的单身人士的限制。此外，找到了针对NRT块代码的填充半径和单胎。
Given $[n]=\{1,2,\ldots,n\}$, a partial order $\preceq$ on $[n]$, a label map $π: [n] \rightarrow \mathbb{N}$ defined by $π(i) = k_i$ with $\sum_{i=1}^{n}π(i) = N$, the direct sum $ \mathbb{F}_{q}^{k_1} \oplus \mathbb{F}_{q}^{k_2}\oplus \ldots \oplus \mathbb{F}_{q}^{k_n} $ of $ \mathbb{F}_q^N $, and a weight function $w$ on $ \mathbb{F}_q $, we define a poset block metric $d_{(P,w,π)}$ on $\mathbb{F}_{q}^{N}$ based on the poset $P=([n],\preceq)$. The metric $d_{(P,w,π)}$ is said to be weighted coordinates poset block metric ($(P,w,π)$-metric). It extends the weighted coordinates poset metric ($(P,w)$-metric) introduced by L. Panek and J. A. Pinheiro and generalizes the poset block metric ($(P,π)$-metric) introduced by M. M. S. Alves et al. We determine the complete weight distribution of a $(P,w,π)$-space, thereby obtaining it for $(P,w)$-space, $(P,π)$-space, $π$-space, and $P$-space as special cases. We obtain the Singleton bound for $(P,w,π)$-codes and for $(P,w)$-codes as well. In particular, we re-obtain the Singleton bound for any code with respect to $(P,π)$-metric and $P$-metric. Moreover, packing radius and Singleton bound for NRT block codes are found.
