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

Weight Enumerators and Higher Support Weights of Maximally Recoverable Codes