Combinatorics

Discrete mathematics

Artificial intelligence

Simplicial complex

Class (philosophy)

Mathematics

Computer science

Binary number

Binary code

Arithmetic

IEEE Transactions on Information Theory

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 F 2 + uF 2 by 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 F 2 + uF 2 . 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.

Optimal Few-Weight Codes From Simplicial Complexes