The design of AES algorithm is based on Feistel cipher.
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An AES is not a fiestel cipher because the operations which is carried out in a n AES is not invertible.
It would be difficult to decrypt languages if the operations which is carried out is not invertible.
In any substitution permutation network the rounds are generally invertible that is the AES but in Fiestel ciphers the round function is not invertible.
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