The nonexistence of code words of weight 16 in a projective plane of order 10

AbstractThe weight enumerator of the binary error-correcting code generated by the rows of the incidence matrix of a projective plane of order 10 is completely determined once the numbers of code words of weight 12, 15, and 16 are known. The search for such a projective plane starting from code words of weight 16 can be divided into six cases. In his 1974 Ph.D. thesis at Berkeley, Carter finished the search for four of these cases as well as part of the fifth. This note reports the results of a computer search for the remaining cases. No projective plane of order 10 was found