dueling challenge; written challenge to a duel
A formal written notice challenging someone to a duel. Historical term, now mostly encountered in period fiction or historical contexts.
彼は相手に決闘状を送りつけた。
He sent a dueling challenge to his opponent.
決闘状 is specifically a written challenge to a duel, while 挑戦状 is broader and can be used for any contest, game, or rivalry.
Compound of 決闘 (kettō, 'duel') and 状 (jō, 'letter' or 'document').