On the generalized Hamming weights of hyperbolic codes (Q6580112)

The article under review studies the generalized Hamming weights of hyperbolic codes. Hyperbolic codes improve Reed-Muller codes in the sense that they have the same minimum distance and higher dimension. The generalized Hamming weights of a linear code are a generalization of the minimum distance, and they have found several applications since their introduction in [\textit{V. K. Wei}, IEEE Trans. Inf. Theory 37, No. 5, 1412--1418 (1991; Zbl 0735.94008)].\N\NThe authors study when a hyperbolic code is also a Reed-Muller code, and they prove that the footprint bound is sharp for hyperbolic codes. This means that one can obtain the generalized Hamming weights of hyperbolic codes by computing the footprint bound. Obtaining the exact value of this bound is still an open problem for hyperbolic codes, but the authors give upper and lower bounds that are sharp in some cases.