Title | Classification of Optimal Ternary (r, δ)-Locally Repairable Codes Attaining the Singleton-like Bound |

Publication Type | Conference Paper |

Year of Publication | 2019 |

Authors | Hao, Jie, Shum, Kenneth W., Xia, Shu-Tao, Yang, Yi-Xian |

Conference Name | 2019 IEEE International Symposium on Information Theory (ISIT) |

Date Published | jul |

Keywords | code symbol, coding theory, compositionality, cryptography, error correction codes, Generators, human computer interaction, Indexes, Information security, k, linear code, linear codes, Metrics, optimal ternary (n, optimal ternary (r, optimal ternary LRC, pubcrawl, q-ary LRC, r, resilience, Resiliency, security, Singleton-like bound, Telecommunications, ternary codes, Upper bound, δ)-locally repairable codes, δ)-LRC classification |

Abstract | In a linear code, a code symbol with (r, d)-locality can be repaired by accessing at most r other code symbols in case of at most d - 1 erasures. A q-ary (n, k, r, d) locally repairable codes (LRC) in which every code symbol has (r, d)-locality is said to be optimal if it achieves the Singleton-like bound derived by Prakash et al.. In this paper, we study the classification of optimal ternary (n, k, r, d)-LRCs (d \textbackslashtextgreater 2). Firstly, we propose an upper bound on the minimum distance of optimal q-ary LRCs in terms of the field size. Then, we completely determine all the 6 classes of possible parameters with which optimal ternary (n, k, r, d)-LRCs exist. Moreover, explicit constructions of all these 6 classes of optimal ternary LRCs are proposed in the paper. |

DOI | 10.1109/ISIT.2019.8849762 |

Citation Key | hao_classification_2019 |