An enumeration of 1-perfect ternary codes

We study codes with parameters of the ternary Hamming $(n=(3^m-1)/2,3^{n-m},3)$ code, i.e., $1$-perfect codes. The rank code is defined to be dimension its affine span. characterize $n-m+1$, count their number, and prove that all such can obtained from each other by a sequence two-coordinate switchings. enumerate length $13$ concatenation lengths $9$ $4$; we find there are $93241327$ equivalence classes Keywords: perfect codes, concatenation, switching.