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Graphs related to -dimensional simplex codes
Mariusz Kwiatkowski, Mark Pankov
We give a complete description of the distance relation on the graph of -ary simplex codes of dimension . This is a connected graph of diameter . For every vertex we deter…
Triangulations with homogeneous zigzags
Mariusz Kwiatkowski, Mark Pankov, Adam Tyc
We investigate zigzags in triangulations of connected closed -dimensional surfaces and show that there is a one-to-one correspondence between triangulations with homogeneous zig…
The graphs of projective codes
Mariusz Kwiatkowski, Mark Pankov, Antonio Pasini
Consider the Grassmann graph formed by -dimensional subspaces of an -dimensional vector space over the field of elements () and denote by the restrict…
Chow's theorem for linear codes
Mariusz Kwiatkowski, Mark Pankov
Let be the Grassmann graph formed by -dimensional subspaces of an -dimensional vector space over the finite field consisting of elements and…
On the distance between linear codes
Mariusz Kwiatkowski, Mark Pankov
Let be an -dimensional vector space over the finite field consisting of elements and let be the Grassmann graph formed by -dimensional subspaces of , $1…
Isometric embeddings of polar Grassmannians and metric characterizations of their apartments
Mariusz Kwiatkowski, Mark Pankov
We describe isometric embeddings of polar Grassmann graphs formed by non-maximal singular subspaces. In almost all cases, they are induced by collinearity preserving injections of…