Linear codes associated with geometric structures
The author studies some codes obtained from geometric structures. Let S be the point set of the structure and let B be the set of blocks. Then he gives the following two codes: I) Code V is spanned by the characteristic functions of the blocks. II) \(H=\{X\in P(S)| \forall_{C\in B}| X\cap C| mod 2\) is constant\(\}\). K is the code obtained by considering the characteristic functions of the elements of H. He restates some results on dimension and minimum distance of the codes obtained by taking for (S;B) the projective plane. Furthermore he states some results (which he proved in another paper) on the dimension and minimum distance of the codes obtained by taking for (S;B): \(S=set\) of lines in PG(r,q) (AG)r,q)), \(B=set\) of stars of lines in PG(r,q) (AG(r,q)). (A star is the set of lines going through a fixed point).
codes obtained from geometric structures
scientific article; zbMATH DE number 4045639