Array Codes for Functional PIR and Batch Codes

A functional PIR array code is a coding scheme which encodes some s information bits into t × m such that every linear combination of the has k mutually disjoint recovering sets. Every set consists array’s columns while it allowed to read at most l encoded from column in order receive requested bits. Functional batch codes impose stronger property where multiset request combinations Locality demand size restrained be r. Given values s, k, t, l, r, goal this paper study optimal value number these exist. Several lower bounds are presented as well explicit constructions for several parameters.