On the Linear Programming Bound for Lee-codes

Abstract: Finding the largest code with a given minimum distance is one of the most basic problems in coding theory. In this paper, we study the linear programming bound for codes in the Lee metric. We introduce refinements on the linear programming bound for linear codes in the Lee metric, which give a tighter bound for linear codes. We also discuss the computational aspects of the problem and introduce a more compact program by the obtained refinements, and a recursive method for computing the so-called Lee-numbers, which are important in the computation of the linear programming bound.