2019/10/10 by Yansheng Wu, Xiaomeng Zhu, Wu, Yansheng +3 · 4 citations
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Finite Group Theory Research #cs.IT #graph theory and CDMA systems #math.IT
paper · pdf · doi:10.48550/arxiv.1910.04334
17 pages, To appear in IEEE IT
arxiv created 2019/10/10 · arxiv updated 2019/10/11
Recently, some infinite families of binary minimal and optimal linear codes are constructed from simplicial complexes by Hyun \em et al. Inspired by their work, we present two new constructions of codes over the ring \Bbb F2+u\Bbb F2 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 \Bbb F2+u\Bbb F2. 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.