Designs and their codes
Codes from Veronese and Segre embeddings and Hamada's formula
Journal of Combinatorial Theory Series A
Rigidity theorems for partial linear spaces
Journal of Combinatorial Theory Series A
On the code generated by the incidence matrix of points and hyperplanes in PG(n,q) and its dual
Designs, Codes and Cryptography
On the code generated by the incidence matrix of points and k-spaces in PG(n,q) and its dual
Finite Fields and Their Applications
Recent progress in algebraic design theory
Finite Fields and Their Applications
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In this article, we determine the words of minimum weight in the code of the incidence system of s- versus t-flats in a finite projective space. Our proof depends on a few combinatorial results on the geometry of flats which may be of independent interest. We also give bounds for the minimum weight of the dual of this code and show that they are attained in many cases. The lower bound is a consequence of a general result on the dual code of an incidence system.