Direct quote from Marx & Engels, The Communist Manifesto?
Lenin said commuinism was Soviet power plus electrification.
As the sort of lefty geeky side note I love, communism didn't really exist from around the 1850s until 1918. When Marx and Engels were writing the Manifesto, the term "communist" tended to be applied to the type of socialist who believed in working through the working class, whereas "socialist" was generally applied to bourgeois reformers trying to persuade governments to implement socialism (Owen, Fourier, St Simon and so on). In the 1850's the "Communist" term fell out of use and "social democrat" became the term for socialists of the Marxist variety.
The Russian Marxist party, founded in 1898 was the Russian Social Democratic Labour Party and it was only after WW1 when Lenin wanted to distinguish his brand of revolutionary conspiratorial voluntantarist Marxism from the mainstream variety that such people started to call themselves Communists again. The RSDLP (or at least it's Bolshevik wing) then became the Communist Party and the Communist International was founded in 1919 to gather such people togerther on a worldwide basis.