Minimal codes in abelian group algebras

In this paper we show that two minimal codes $\text{M}$₁ and $\text{M}$₂ in the group algebra $\text{F}$₂[G] have the same (Hamming) weight distribution if and only if there exists an automorphism θ of G whose linear extension to $\text{F}$₂[G] maps $\text{M}$₁ onto $\text{M}$₂. If θ(M₁) = M₂, then $\text{M}$₁ and $\text{M}$₂ are called equivalent. We also show that there are exactly τ(l) inequivalent minimal codes in $\text{F}$₂[G], where ? is the exponent of G, and τ(?) is the number of divisors of ?.