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The Sriwijaya Air disappeared from radars four minutes into its journey to Pontianak in West Kalimantan province.
It is thought to have dropped more than 3,000m (10,000ft) in less than a minute, according to flight tracking website Flightradar24.com.
Witnesses said they had seen and heard at least one explosion.
"The plane fell like lightning into the sea and exploded in the water," he said.
"It was pretty close to us, the shards of a kind of plywood almost hit my ship."