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pro vyhledávání: '"Golomb rulers"'
A set $\{a_i\:|\: 1\leq i \leq k\}$ of non-negative integers is a Golomb ruler if differences $a_i-a_j$, for any $i \neq j$, are all distinct.All finite Sidon sets are Golomb rulers, and vice versa. A set of $I$ disjoint Golomb rulers (DGR) each bein
Externí odkaz:
http://arxiv.org/abs/2409.14409
Autor:
Gordon, Daniel M.
A $(v,k,\lambda)$-difference set in a group $G$ of order $v$ is a subset $\{d_1, d_2, \ldots,d_k\}$ of $G$ such that $D=\sum d_i$ in the group ring ${\mathbb Z}[G]$ satisfies $$D D^{-1} = n + \lambda G,$$ where $n=k-\lambda$. In other words, the nonz
Externí odkaz:
http://arxiv.org/abs/2408.16721
A Golomb ruler is a sequence of integers whose pairwise differences, or equivalently pairwise sums, are all distinct. This definition has been generalized in various ways to allow for sums of h integers, or to allow up to g repetitions of a given sum
Externí odkaz:
http://arxiv.org/abs/2308.11118
We introduce and study a family of rate-compatible Low-Density Parity-Check (LDPC) codes characterized by very simple encoders. The design of these codes starts from simplex codes, which are defined by parity-check matrices having a straightforward f
Externí odkaz:
http://arxiv.org/abs/2309.14917
Akademický článek
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Autor:
Buratti, Marco, Stinson, Douglas R.
We prove new existence and nonexistence results for modular Golomb rulers in this paper. We completely determine which modular Golomb rulers of order $k$ exist, for all $k\leq 11$, and we present a general existence result that holds for all $k \geq
Externí odkaz:
http://arxiv.org/abs/2007.01908
Autor:
Buratti, Marco, Stinson, Douglas R.
We define a new type of Golomb ruler, which we term a resolvable Golomb ruler. These are Golomb rulers that satisfy an additional "resolvability" condition that allows them to generate resolvable symmetric configurations. The resulting configurations
Externí odkaz:
http://arxiv.org/abs/2004.04088
Publikováno v:
IEEE Access, Vol 9, Pp 65482-65489 (2021)
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 construction
Externí odkaz:
https://doaj.org/article/9621d5f4748b4a299a2286bf0204545a
Publikováno v:
IEEE Access, Vol 9, Pp 118042-118050 (2021)
A set of positive integers $A$ is called a Golomb ruler if the difference between two distinct elements of $A$ are different, equivalently if the sums of two elements are different ( $B_{2}$ set, Sidon set). An extension of this concept is to conside
Externí odkaz:
https://doaj.org/article/04adff75ba0d419a9b0b69e3706911df
Autor:
Inseon Kim, Hong‐Yeop Song
Publikováno v:
Electronics Letters, Vol 58, Iss 15, Pp 582-584 (2022)
Abstract In this paper, an algebraic construction of regular QC‐LDPC codes by using the modular multiplication table mod P and Golomb rulers are proposed. It is proved that the proposed QC‐LDPC codes based on a Golomb ruler of length L have girth
Externí odkaz:
https://doaj.org/article/4b6e7fc8378b44a5a12882dff752972d