We prove the equivalence of several definitions of extended $1$-perfect bitrades in the Hamming graph $H(n,q)$ and prove the nonexistence of such bitrades for odd $n$.

翻译：我们证明哈明图$H(n,q)中扩大的美元完美两极交易的若干定义是等同的,并证明单价美元不存在这种两极交易。