New Results on Asymmetric Single Correcting Codes of Magnitude Four

作者：Xie, Derong; Luo, Jinquan^*

来源：IEEE Transactions on Information Theory, 2021, 67(8): 5079-5087.

DOI：10.1109/TIT.2021.3085754

• Asymmetric error
• flash memories
• limited magnitude error
• single error

An error model with asymmetric single error with magnitude four is considered. In this paper, the constructions of codes correcting single error of magnitude four over Z(2a3br) are studied which is equivalent to construct B-1[4](2(a) 3(b)r) sets. Firstly, we reduce the construction of a maximal size B-1[4](2(a) 3(b)r) set for a >= 4 and gcd(r, 6) = 1 to the construction of a maximal size B-1[4](2(a-3) 3(b)r) set. Furthermore, we will show that maximal size B-1[4](8 center dot 3(b)r) sets can be reduced to maximal size B-1[4](3(b)r) sets and also give lower bounds of maximal size B-1[4](12r) and B-1[4](2 center dot 3(b)r) sets. Finally, we give a necessary and sufficient condition on the existence of perfect B1[4](p) set for prime p.