Binary Weight Spectrum of the Extended $[2^m,5]$ Reed–Solomon Code and its Dual Code

We consider the extended $[2^m,5]$ Reed–Solomon code over $GF(2^m)$ and its binary image determined by the choice of a basis $\beta_1,\beta_2,\dots,\beta_m$ over $GF(2)$. The weight spectrum of the binary image for a certain class of bases is computed.