Pairwise inequivalence conjecture for Kassami APN design codes

Let $n\geq5$ be odd, and let

$$I_n=\left\{i:1\leq i\leq\frac{n-1}{2},\ \gcd(i,n)=1\right\}.$$

Let $\phi(n)$ denote Euler's totient function. Kassami-code inequivalence conjecture. The $\frac{\phi(n)}2$ binary linear codes $\mathsf{C}_2(\mathbb{KA}_{n,i})$, for $i\in I_n$, are pairwise inequivalent. The source does not provide a general proof or resolution.