Extended Integrated Interleaved Codes over any Field with Applications to Locally Recoverable Codes
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Integrated Interleaved (II) and Extended Integrated Interleaved (EII) codes are a versatile alternative for Locally Recoverable (LRC) codes, since they require fields of relatively small size. II and EII codes are generally defined over Reed-Solomon type of codes. A new comprehensive definition of EII codes is presented, allowing for EII codes over any field, and in particular, over the binary field GF(2). It is shown that the traditional definition of II and EII codes is a special case of the new definition. Properties of the codes are presented as well, in particular, an iterative decoding algorithm on rows and columns generalizing the iterative decoding algorithm of product codes. The problem of ordering the symbols such that the maximum length of a correctable burst is achieved is considered as well.
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