Weight Enumerators and Higher Support Weights of Maximally Recoverable Codes

Abstract

In this paper, we establish the matroid structures corresponding to data-local and local maximally recoverable codes (MRC). The matroid structures of these codes can be used to determine the associated Tutte polynomial. Greene proved that the weight enumerators of any code can be determined from its associated Tutte polynomial. We will use this result to derive explicit expressions for the weight enumerators of data-local and local MRC. Also, Britz proved that the higher support weights of any code can be determined from its associated Tutte polynomial. We will use this result to derive expressions for the higher support weights of data-local and local MRC with two local codes.

arXiv comment19 pages

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Cited by in corpus (5)

• Erasure Coding for Distributed Storage: An Overview
• On the Weight Hierarchy of Locally Repairable Codes
• Communication Cost for Updating Linear Functions when Message Updates are Sparse: Connections to Maximally Recoverable Codes
• Erasure Codes for Distributed Storage: Tight Bounds and Matching Constructions
• The independence number of the Birkhoff polytope graph, and applications to maximally recoverable codes