New Quaternary Linear Codes with Covering Radius 2,

A new quaternary linear code of length 19, codimension 5, and covering radius 2 is found in a computer search using tabu search, a local search heuristic. Starting from this code, which has some useful partitioning properties, different lengthening constructions are applied to get an infinite family of new, record-breaking quaternary codes of covering radius 2 and odd codimension. An algebraic construction of covering codes over alphabets of even characteristic is also given.