Almost Difference Sets From Singer Type Golomb Rulers
David Fernando Daza Urbano, Carlos Andrés Martos Ojeda, Carlos A. Trujillo · IEEE Access · 2021
Let$G$be an additive group of order$v$. A$k$-element subset$D$of$G$is called a$(v, k, \lambda, t)$-almost difference set if the expressions$g-h$, for$g$and$h$in$D$, represent$t$of the non-identity elements in$G$exactly$\lambda $times and every other non-identity element$\lambda + 1$times. Almost difference sets are highly sought after as they can be used to produce functions with optimal nonlinearity, cyclic codes, and sequences with three-level autocorrelation. A set of positive integers$A$is called a Golomb ruler if the difference between two distinct elements of$A$are different. In this paper, we use Singer type Golomb rulers to construct new families of almost difference sets. Additionally, we constructed 2-adesigns from these almost difference sets.