  Quantum resources and protocols are known to outperform their classical
counterparts in variety of communication and information processing tasks.
Random Access Codes (RACs) are one such cryptographically significant family of
bipartite communication tasks, wherein, the sender encodes a data set
(typically a string of input bits) onto a physical system of bounded dimension
and transmits it to the receiver, who then attempts to guess a randomly chosen
part of the sender's data set (typically one of the sender's input bits). In
this work, we introduce a generalization of this task wherein the receiver, in
addition to the individual input bits, aims to retrieve randomly chosen
functions of sender's input string. Specifically, we employ sets of mutually
unbiased balanced functions (MUBS), such that perfect knowledge of any one of
the constituent functions yields no knowledge about the others. We investigate
and bound the performance of (i.) classical, (ii.) quantum prepare and measure,
and (iii.) entanglement assisted classical communication (EACC) protocols for
the resultant generalized RACs (GRACs). Finally, we detail the case of GRACs
with three input bits, find maximal success probabilities for classical,
quantum and EACC protocols, along with the effect of noisy quantum channels on
the performance of quantum protocols. Moreover, with the help of this case
study, we reveal several characteristic properties of the GRACs which deviate
from the standard RACs.
