Codes associated with the odd graphs

Linear codes arising from the row span over any prime field F p of the incidence matrices of the odd graphs O k 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 O 2 (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 P G 3 ( F 2 ) , which leads to a correspondence between the edges and vertices of O 2 with the points and a collection of ten lines of P G 3 ( F 2 ) , consistent with the codes. udy 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 ( O k ) .