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Optimal Locally Recoverable Codes With Hierarchy From Nested F-Adic Expansions | IEEE Journals & Magazine | IEEE Xplore

Optimal Locally Recoverable Codes With Hierarchy From Nested F-Adic Expansions


Abstract:

In this paper we construct new optimal hierarchical locally recoverable codes. Our construction is based on a combination of the ideas of Ballentine et al., (2019) and Sa...Show More

Abstract:

In this paper we construct new optimal hierarchical locally recoverable codes. Our construction is based on a combination of the ideas of Ballentine et al., (2019) and Sasidharan et al., (2015) 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 wider 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.
Published in: IEEE Transactions on Information Theory ( Volume: 69, Issue: 11, November 2023)
Page(s): 6981 - 6988
Date of Publication: 24 July 2023

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