Abstract
The primary application of codes with locality and availability in
distributed storage is for data recovery in case that data are lost on
some damaged servers. Locality enables the recovery of lost data by
contacting only a restricted number of remaining servers. Availability
means that more than one subset of servers providing locality is
available for data recovery for each server. The secondary application
of these codes in distributed storage is to allow access to hot data in
times of high demand. In this paper it is shown that the binary linear
[14, 4, 7] code has locality 2 and availability 6 and it can be
interpreted as a three-dimensional graph obtained from a [7, 3, 4]
Simplex code. It is achieving upper bounds on basic parameters for codes
with all-symbols locality and availability. This code can be a building
element of more complex codes with scalability inspired by
three-dimensional structures. The availability spectrum is introduced as
a tool for analyzing codes with locality and availability.