摘要 : Based on theoretical neuroscience, G. Cotardo and A. Ravagnani (2022) introduced a class of asymmetric binary codes called combinatorial neural codes (CN codes for short), with a “matched metric” $\delta _{r}$ called asymmetric ... 展开 Based on theoretical neuroscience, G. Cotardo and A. Ravagnani (2022) introduced a class of asymmetric binary codes called combinatorial neural codes (CN codes for short), with a “matched metric” $\delta _{r}$ called asymmetric discrepancy, instead of the Hamming distance $d_{H}$ for usual error-correcting codes. They also presented the Hamming, Singleton and Plotkin bounds for CN codes with respect to $\delta _{r}$ and asked how to construct CN codes ${\mathcal C}$ with large size $| {\mathcal C}|$ and minimum $\delta _{r}({\mathcal C})$ . In this paper, we first show that a binary code ${\mathcal C}$ reaches one of the above bounds for $\delta _{r}({\mathcal C})$ if and only if ${\mathcal C}$ reaches the corresponding bounds for $d_{H}$ and $r$ is sufficiently close to 1. This means that all optimal CN codes come from the usual optimal codes. Then, we present several constructions of CN codes with good and flexible parameters $(n,K, \delta _{r}({\mathcal C}))$ by using bent functions. 收起