On the equivalence between the B-Code constructions and perfect one-factorizations

Abstract

The B-Code is a class of MDS array code with optimal properties for RAID 6. Xu et al. proposed an open problem in 1999: Are the B-Code constructions strongly equivalent to perfect one-factorizations of a graph? In this paper, we show that the constructions of the B-Code of length l are equivalent to perfect one-factorizations of a l-regular graph on l + r vertices, where l is an integer not smaller than 4, and r is equal to 1 for an odd l or 2 for an even l.