Infinite families of p-ary distance optimal linear codes for odd prime numbers p

In this paper, we consider infinite families of linear codes associated to down sets over the ring R= Fp + uFp for u2 = 0 and p an odd prime number. We determine the Lee weight distributions for these codes when the down sets are generated by a single or two maximal elements. When applying the Gray map to such linear codes, we have identified (p-1)(2p-1) classes of p-ary distance optimal linear codes, and some of which meet the Griesmer bound.