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T-Code: 3-Erasure Longest Lowest-Density MDS Codes
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DOI：10.1109/JSAC.2010.100218.png)
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Abstract
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In this paper, we study longest lowest-density MDS codes, a simple kind of multi-erasure array code with optimal redundancy and minimum update penalty. We prove some basic structure properties for longest lowest-density MDS codes. We define a perfect property for near-resolvable block designs (NRBs) and establish a bijection between 3-erasure longest lowest-density MDS codes (T-Codes) and perfect NRB(3k + 1, 3, 2)s. We present a class of NRB(3k + 1, 3, 2) s, and prove that it produces a family of T-Codes. This family is infinite assuming Artin's Conjecture. We also test some other NRBs and find some T-Code instances outside of this family.
Keywords:
3-erasure correcting codes
parity array codes
near-resolvable design
perfect one-factorization
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