A Linear Programming bound for Unequal Error Protection codes

In coding theory, it is important to calculate an upper bound for the size of codes given the length and minimum distance. The linear programming (LP) bound is known as a good upper bound for the size of codes. On the other hand, Unequal error protection (UEP) codes have been studied in coding theory. In UEP codes, a codeword has special bits which are protected against a greater number of errors than other bits. In this paper, we propose a LP bound for UEP codes. Firstly, we generalize the distance distribution (or weight distribution) of codes. Under the generalization, we lead to the LP bound for UEP codes. And we show a numerical example of the LP bound for UEP codes. Lastly, we compare the proposed bound with a modified Hamming bound.