Abstract
Linear codes arising from the row span over any prime field Fp of the incidence matrices of the odd graphs Ok for k≥2 are examined and all the main parameters obtained. A study of the hulls of these codes for p=2 yielded that for O2 (the Petersen graph), the dual of the binary hull from an incidence matrix is the binary code from points and lines of the projective geometry PG3(F2), which leads to a correspondence between the edges and vertices of O2 with the points and a collection of ten lines of PG3(F2), consistent with the codes.The study also gives the dimension, the minimum weight, and the nature of the minimum words, of the binary codes from adjacency matrices of the line graphs L(Ok).
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