Regular Multiset Combinatorial Batch Codes over Vector Spaces

A multiset combinatorial batch code (MCBC) over vector space consists of a set of subspaces of
$\mathbb{F}_{q}^{n}$
, each corresponding to a server, such that requests consisting of
$t$
dimensional subspaces, can be retrieved from the servers. The code is said to be regular if all the subspaces in the code have the same dimension. The aim is to find the minimum number of total storage, and also the minimum number of servers in the regular case, fixing other parameters. In this paper, we provide bounds and constructions for this new class of batch codes.