Work

Rotating Binaries

Year: 2022

Type: article

Abstract: This paper investigates the behavior of rotating binaries. A rotation by r digits to the left of a binary number B exhibits in particular cases the divisibility l∣N1(B)·r+1, where l is the bit-length of B and N1(B) is the Hamming weight of B, that is the number of ones in B. The integer r is called the left-rotational distance. We investigate the connection between this rotational distance, the length, and the Hamming weight of binary numbers. Moreover, we follow the question under which circumstances the above-mentioned divisibility is true. We have found out and will demonstrate that this divisibility occurs for kn+c cycles.

Source: AppliedMath

DOI: 10.3390/appliedmath2010005

Authors: Anant Gupta, Idriss J. Aberkane, Sourangshu Ghosh, Adrian Abold, Alexander Rahn, Eldar Sultanow

Institutions: Georgia Institute of Technology, UNESCO, Indian Institute of Technology Kharagpur, Friedrich-Alexander-Universität Erlangen-Nürnberg, University of Bamberg, University of Potsdam

Language: English

Topic: Coding theory and cryptography

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,047

OpenAlex ID: W4210697516

FWCI: 0.241

Cites: 11

Cited by: 5

Related to: 10