Abstract: In this work, the linear span codes over GF(2) and GF (5) of a possible projective plane of 

order 10 are investigated. In the case GF (2), some configurations are characterized for vectors of weight 

16, the smallest Hamming weight for which the count of vectors is unknown. In the case GF (5), it is 

shown that the vectors of minimum weight excluding the lines have weight 20, amounting to a 

determination of about a quarter of the unknown coefficients in the Lee weight enumerator of the code. 

The method used to obtain this result is applied to the linear span code over GF (5) of the projective 

plane of order 5 whose Lee weight enumerator polynomial is determined completely. 

Key words: Finite projective plane, incidence matrix, linear codes over GF (2) and GF (5), self-dual, 

Lee weight enumerator, view, contribution.