Optimal Few-weight Codes From Simplicial Complexes
Wu Yansheng, Zhu Xiaomeng, Yue Qin. Arxiv 2019
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 \(\Bbb F_2+u\Bbb F_2\) 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 \(\Bbb F_2+u\Bbb F_2\). 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.
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