Optimal locally recoverable codes with hierarchy from nested F-adic expansions

07/21/2022
by   Austin Dukes, et al.
0

In this paper we construct new optimal hierarchical locally recoverable codes. Our construction is based on a combination of the ideas of <cit.> with an algebraic number theoretical approach that allows to give a finer tuning of the minimum distance of the intermediate code (allowing larger dimension of the final code), and to remove restrictions on the arithmetic properties of q compared with the size of the locality sets in the hierarchy. In turn, we manage to obtain codes with a wide set of parameters both for the size q of the base field, and for the hierarchy size, while keeping the optimality of the codes we construct.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset