New Results on Asymmetric Single Correcting Codes of Magnitude Four
Derong Xie, Jinquan Luo · IEEE Transactions on Information Theory · 2021
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 \mathbb Z2a3brare studied which is equivalent to construct B1[4](2a3br) sets. Firstly, we reduce the construction of a maximal size B1[4](2a3br) set for a ≥ 4 and gcd(r,6)=1 to the construction of a maximal size B1[4](2a-33br) set. Furthermore, we will show that maximal size B1[4](8·3br) sets can be reduced to maximal size B1[4](3br) sets and also give lower bounds of maximal size B1[4](12r) and B1[4](2·3br) sets. Finally, we give a necessary and sufficient condition on the existence of perfect B1[4](p) set for prime p.