The MySQL full text search always uses the MyISAM engine limits for the min and max search strings, even when using the InnoDB engine.

fulltext_mysql.php looks up the ft_max_word_len and ft_min_word_len settings when determining what the maximum and minimum search strings are. However, these are only valid for the MyISAM engine. For the InnoDB engine the settings are innodb_ft_max_token_size and innodb_ft_min_token_size.