This tag has several uses: a Japanese psych/noise rock style (and a Syracuse, NY scene derived from this - see no-core), and North Carolina HxC..

1) The work of early '80s Japanese bands like Boredoms has been referred to as No Core (from their song "No Core Punk"). In this sense one might suppose it to be an extension of No Wave, the music being similarly spazzed-out punk-based music but more intense and abstract psych rock; noisecore in a sense though not necessarily connected to hardcore.

2) No Core was a designation used by early 80's North Carolina hardcore punk bands, presumably with the first letters corresponding with state's initials. There was a compilation tape released under this name as well as other punk albums and publications. No Core could also refer to later North Carolina bands that have some connection to that early regional punk scene.

3) The Syracuse usage is associated with bands who appeared in mplockwood's No-Core podcast, which can be found at http://www.no-core.net/podcast/ The correct spelling for this broadcast designation includes a hyphen. See No-Core.