Papers by David Fernando Daza Urbano
IEEE Access, 2021
A set of positive integers A is called a g-Golomb ruler if the difference between two distinct el... more A set of positive integers A is called a g-Golomb ruler if the difference between two distinct elements of A is repeated up to g times. This definition is a generalization of the Golomb ruler (g = 1). In this paper, we obtain new constructions for g-Golomb rulers from Golomb rulers, using these constructions we find some suboptimal 2 and 3-Golomb rulers with up to 124 marks and we prove two theorems related to extremal functions associated with this sets improving already known results.
Non‐existence of (pm,k,1) difference sets
Electronics Letters, 2021
IEEE Access
Let G be an additive group of order v. A k-element subset D of G is called a (v, k, λ, t)-almost ... more Let G be an additive group of order v. A k-element subset D of G is called a (v, k, λ, t)-almost difference set if the expressions gh, for g and h in D, represent t of the non-identity elements in G exactly λ times and every other non-identity element λ + 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.
IEEE Access, 2021
A set of positive integers A is called a <inline-formula> <tex-math notation="LaTeX... more A set of positive integers A is called a <inline-formula> <tex-math notation="LaTeX">$g$ </tex-math></inline-formula>-Golomb ruler if the difference between two distinct elements of A is repeated up to <inline-formula> <tex-math notation="LaTeX">$g$ </tex-math></inline-formula> times. This definition is a generalization of the Golomb ruler <inline-formula> <tex-math notation="LaTeX">$(g = 1)$ </tex-math></inline-formula>. In this paper, we obtain new constructions for <inline-formula> <tex-math notation="LaTeX">$g$ </tex-math></inline-formula>-Golomb rulers from Golomb rulers, using these constructions we find some suboptimal 2 and 3-Golomb rulers with up to 124 marks and we prove two theorems related to extremal functions associated with this sets improving already known results.
IEEE Access
Let G be an additive group of order v. A k-element subset D of G is called a (v, k, λ, t)-almost ... more Let G be an additive group of order v. A k-element subset D of G is called a (v, k, λ, 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 λ times and every other non-identity element λ + 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.
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Papers by David Fernando Daza Urbano