We know that general palindromes cannot be decided by a DFA.Howeve if you restrict to case of even length palindromes, does a DFA need exactly $2^{2k}$ states where $2k$ is length of palindrome the language needs to accept?I get this as lower bound from Myhill Nerode aplication.From answers below, my lower bound is wrong. What is the correct bound from Myhill Nerode?How do you show the upper bound?
Palindrome of fixed length
automata;finite automata;dfa