Optimal Few-Weight Codes From Simplicial Complexes
Yansheng Wu, Xiaomeng Zhu, Qin Yue · IEEE Transactions on Information Theory · 2019
Recently, some infinite families of binary minimal and optimal linear codes were constructed from simplicial complexes by Hyun et al. Inspired by their work, we present two new constructions of codes over the ring F2+ uF2by employing simplicial complexes. When the simplicial complexes are all generated by a maximal element, we determine the Lee weight distributions of two classes of the codes over F2+ uF2. Our results show that the codes have few Lee weights. Via the Gray map, we obtain an infinite family of binary codes meeting the Griesmer bound and a class of binary distance optimal codes.