Multiple-Layer Integrated Interleaved Codes: A Class of Hierarchical Locally Recoverable Codes

The traditional definition of Integrated Interleaved (II) codes generally assumes that the component nested are either Reed-Solomon (RS) or shortened codes. By taking general classes codes, we present a recursive construction Extended (EII) into multiple layers, problem brought attention in literature for II layer approach allows hierarchical scheme where each code provides different locality. In particular, erasure-correcting capability new and show they ideally suited as Locally Recoverable (LRC) due to their locality small finite field required by construction. Properties EII like minimum distance dimension, well erasure decoding algorithms, parity-check matrices performance analysis, provided illustrated with examples. Finally, will observe high have low density.