Few-weight codes over a non-chain ring associated with simplicial complexes and their distance optimal Gray image

Abstract

In this paper, we construct new infinite families of codes over the ring R=F2+uF2+vF2+uvF2,u2=v2=0,uv=vu by employing simplicial complexes. When the simplicial complexes are all generated by a single maximal element, we compute the Lee weight distributions of these classes of codes. By the Gray map, we show that some classes of codes are minimal and some classes of these codes are distance optimal.