Muichimonji (無一文字, lit. "Nothingness") is Mitsurugi's new primary weapon in Soulcalibur V. It replaces Shishi-Oh, which Mitsurugi lost in a fateful duel with a Battōjyutsu swordswoman 17 years ago, but managed to gain victory by punching her stomach.
After he returned home to Bizen, Mitsurugi encountered a rather pathetic katana set behind a tag identifying it as 'Ichimonji'. While no respectable blacksmith would ever admit to creating such a weapon, Mitsurugi had come to the realization that the strength of one's weapon is just for show. A warrior's true strength comes from within.
Looking at the sorry excuse for a katana, Mitsurugi was reminded of a younger him, a hopelessly ambitious boy who was the son of a simple farmer, yet gave himself the name of 'Heishiro MItsurugi' as a sign of his conviction to become an elite samurai. "It's a worthless katana, but it suits my style..."
After purchasing the blade for next to nothing, Mitsurugi renamed the sword 'Muichimonji'.
Historical Ichimonji were in fact Nihontô from the Kôtô and Shinto era, signed with the character (monji) for 1 (ichi), a simple horizontal lign. Because a sword struck need to be right in order to be powerfull. Especially in the case of Shomen-uchi strike, who allows the technique of Kabuto-wari (helmet splitting), if the stroke is not right, it will loose a bit of strength, and fail to split the helmet or inflict minor wounds. Japanese swordsmiths who signed in such a way, at that time, were meant to give confidence to the warrior while he was stepping on the battlefield to behead enemies and gain honor and recognition among his peers.
A famous kind of Ichimonji swords are the Kiku'ichimonji, legacy of Emperor Go-Toba-Tennô, signed with the Imperial Chrysanthemum (Kiku).
Indeed, few Kôtô were signed (especially in Yamatô-den, who were furniture for Buddhist temples and Sôhei), it is only in the Edo era that long and flamboyant signature became standard, despite the fact signatures were always thought to be the pride of the smith and confidence in his work.
What Mitsurugi may meant by a "sorry excuse for a katana" is unclear, but this Muichimonji was probably a sword among those mass producted in the Shintô period, for the legions of Ashigaru all around Japan at that time. They were of a lower quality, with lesser easthetics, sharpness, cutting prowess, edge retention and battle endurance (and since Japanese Swords are often quite thin, they could broke easily, unlike superior blades made during the Kôtô era), though they were still of good quality in medieval standards (and far better than modern mass produced chinese crap).
Also, the name Muichimonji may be some "Mitsurugi special humor" meaning that it does not live to it's name. "Mu" is a Buddhist term meaning "nothingness", "No" or "do not". It is also similar to Kû (sunyata) who is said to represent the "ultimate nature of reality".