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

Abstract

In this paper, we consider infinite families of linear codes associated to down sets over the ring R = Fp + uFp for u^2= 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.