On a family of Abelian codes and their state complexities
We study Reed-Muller codes and "Berman " codes as Abelian codes. We show that the duals of Berman codes and Reed-Muller codes fan be considered as belonging to the same family of Abelian codes. We also determine the minimum distance and state complexity (SC) of the duals of Berman codes. Each of the classical parameters generalizes that of Reed-Muller codes in the obvious way but the state complexity does not. We conclude by comparing the asymptotic behavior of the SC of the duals of Berman codes with that of the obvious generalization of the SC of Reed-Muller codes.
abelian codes state complexity reed-muller codes ideal generators