A Family of Codes With Locality Containing Optimal Codes

Locally recoverable codes were introduced by Gopalan <italic>et al.</italic> in 2012, and in the same year Prakash <italic>et al.</italic> introduced the concept of codes with locality, which are a type of locally recoverable codes. In this work we introduce a new family of c...

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Bibliographic Details
Main Authors: Bruno Andrade, Cicero Carvalho, Victor G. L. Neumann, Antonio C. P. Veiga
Format: Article
Language:English
Published: IEEE 2022-01-01
Series:IEEE Access
Subjects:
Online Access:https://ieeexplore.ieee.org/document/9749211/
Description
Summary:Locally recoverable codes were introduced by Gopalan <italic>et al.</italic> in 2012, and in the same year Prakash <italic>et al.</italic> introduced the concept of codes with locality, which are a type of locally recoverable codes. In this work we introduce a new family of codes with locality, which are subcodes of a certain family of evaluation codes. We determine the dimension of these codes, and also bounds for the minimum distance. We present the true values of the minimum distance in special cases, and also show that some elements of this family are &#x201C;optimal codes&#x201D;, as defined by Prakash <italic>et al.</italic>
ISSN:2169-3536