Daicon IV was a sci-fi convention held in 1983, in Osaka, Japan; the 22nd Nihon SF Taikai.
Daicon is a portmanteau of "dai", an alternate reading of the first kanji in the name of the city in which it is held (which means "big/great"), and the first syllable of the English word "convention". However, it is also a deliberate pun, since its name suggests the word daikon, the east Asian giant radish. "Daicon", like the names of most Japanese sci-fi conventions, is always written in the Latin alphabet.
The opening to Daicon IV, made by Gainax (which at the time was called Daicon Film), is a 4:23 cel animated video. The opening to the sci-fi convention was anime. As many kinds of "geek" culture appeal to the typical Otaku, the video has many pop culture references. The animation features the now grown up Daicon III girl fighting a wide selection of creatures from all sorts of science fiction and fantasy movies and novels, including Darth Vader, Eleking from Ultra Seven, the Toho logo, an alien, a Macross VF-1 Valkyrie, a Pern dragon, Aslan, a Klingon battle cruiser, Spider-Man, Taiyou Sentai Sun Vulcan, and a pan across a vast array of hundreds of other characters) as she surfs through the sky on the sword Stormbringer.
This video, although short, clearly marked the otaku subculture for its state-of-the-art animation for 1983. There soon were merchandise and figures of the nameless "Daicon IV bunny-eared girl" who is seen surfing around on a flying sword, Stormbringer, in the video.
In Gainax's 1992 OVA Otaku no Video, a character shows another what are anime and animation techniques, and shows a part of the Daicon IV opening. Additionally, Otaku no Video's very mascot, Misty May, is clearly a reference to the Daicon IV girl.
Another of Gainax's OVAs, FLCL (2000-2001), shows Haruko in episode 5 (Brittle Bullet) dressed in the same bunny suit, flying over a guitar to attack a giant monster. During her attack, she screams "Daicon V!".
The Japanese TV series Densha Otoko (2005) features an opening that is also a clear reference, featuring a girl with bunny ears surfing around on a train with the same background tune, Electric Light Orchestra's "Twilight".