Galois geometries, codes, and new invariants for incidence structures
Tonchev Vladimir D. · NATO science for peace and security series. D, Information and communication security · 2015
The paper discusses a recently discovered tight connection between Galois geometry, linear codes, and incidence matrices, that leads to new invariants for incidence structures. These new invariants admit both an algebraic and a geometric description, and are motivated by the longstanding Hamada conjecture about the minimum rank of the incidence matrices of the classical geometric designs and their use for the construction of majority-logic decodable error-correcting codes.