Number Theoretical Locally Recoverable Codes

04/18/2023

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by   Andrea Ferraguti, et al.

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In this paper we give constructions for infinite sequences of finite non-linear locally recoverable codes 𝒞⊆∏^N_i=1𝔽_q_i over a product of finite fields arising from basis expansions in algebraic number fields. The codes in our sequences have increasing length and size, constant rate, fixed locality, and minimum distance going to infinity.