论文标题
部分可观测时空混沌系统的无模型预测
Array Codes for Functional PIR and Batch Codes
论文作者
论文摘要
功能性PIR数组代码是一种编码方案，该方案将一些$ S $信息位编码到$ t \ times m $阵列中，以便$ s $信息位的每个线性组合都有$ k $相互脱节的恢复集。每个恢复集由一些数组的列组成，而允许从每一列中最多读取$ \ ell $编码的位，以接收信息位的线性组合。功能批处理阵列代码施加了更强的属性，其中每个多键$ k $线性组合的多动请求都有$ k $互机恢复集。 Locality functional array codes demand that the size of every recovering set is restrained to be at most $r$.鉴于$ s，k，t，\ ell，r $的值，本文的目标是研究列数$ m $的最佳值，以便存在这些代码。 Several lower bounds are presented as well as explicit constructions for several of these parameters.
A functional PIR array code is a coding scheme which encodes some $s$ information bits into a $t\times m$ array such that every linear combination of the $s$ information bits has $k$ mutually disjoint recovering sets. Every recovering set consists of some of the array's columns while it is allowed to read at most $\ell$ encoded bits from every column in order to receive the requested linear combination of the information bits. Functional batch array codes impose a stronger property where every multiset request of $k$ linear combinations has $k$ mutually disjoint recovering sets. Locality functional array codes demand that the size of every recovering set is restrained to be at most $r$. Given the values of $s, k, t, \ell,r$, the goal of this paper is to study the optimal value of the number of columns $m$ such that these codes exist. Several lower bounds are presented as well as explicit constructions for several of these parameters.
