The method transmits a long packet of digital data over a poly-phase power line affected by impulsive noise synchronous with phase voltages. Instead of using very complicated coding schemes, starting from the knowledge of the typical power line scenario, useful information is transmitted where noise synchronous with the main signal is absent. Time-intervals of a known or estimated duration during which the poly-phase power line is affected by impulsive noise are determined, and dummy data during the time-intervals, and useful data during other time-intervals free from impulsive noise, are transmitted.