On the Optimal Reconstruction Degree of Fractional Repetition Codes

Fractional repetition (FR) codes form a special class of minimum bandwidth regenerating codes by providing uncoded repairs with a table-based repair model. In this paper, we focus on a lower bound on the reconstruction degree of FR codes, which is the smallest number of storage nodes required for data retrieval. We show that for an FR code with reconstruction degree attaining this lower bound, the corresponding dual FR code is optimal with respect to an upper bound on the file size, and vice versa. Using this duality relationship, we present several families of FR codes with optimal reconstruction degree.