Some New Binary Locally Repairable Codes with Availability based on Golomb Rulers

In this paper, we propose some new binary 5-sequential recovery Locally Repairable Codes (5-seq LRCs) with availability 2 based on Golomb rulers and some well-known technique of generating the parity check matrix for the QC-LDPC codes. The proposed 5-seq LRCs can repair up to 5 erased symbols sequentially within 3 repair time. It can be viewed as an intersection of two LRCs without availability and its code rate is optimal for some cases.