# A problem about Huffman codeword

Under Huffman Encoding, what circumstances codeword length of each character be equal?(suppose number of character is power of 2)

I think if all frequency of characters is same then codeword length of all characters be the same. Surprisingly, if there are two characters that differences between frequency of two characters be $$2$$, and frequency of other be equal then codeword length of all characters be the same.

Main problem is, can i say, for each constant $$c$$, if there are two character that difference of frequency be $$c$$, and all remaining of characters have equal frequency then codeword length of each character be equal?

• My proposition: for each constant $c$, if there are two character that difference of frequency be $c$, and all remaining of characters have equal frequency then codeword length of each character be equal?