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No, you can't.

An index, in MySQL, will either be

  • a BTREE single or multi-column index.

  • a HASH index (available only for MEMORY tables), that can span several columns.

  • a SPATIAL index (available only for MyISAM tables).

  • a FULLTEXT index (available for MyISAM and 5.6.4+ InnoDB tables), that can span several columns of CHAR, VARCHAR or TEXT type.

You can't combine these types.