Fractal digital sums and codes
type: Item
instance of: scholarly article
title: Fractal digital sums and codes
zbMATH Open document ID: 0874.11012
author: Tamás Herendi
author: Robert F. Tichy
author: Peter J. Grabner
published in: Applicable Algebra in Engineering, Communication and Computing
publication date: 1997-11-13T00:00:00Z
review text: The aim of this paper is to study digital sums of the type \[ S_p(N)= \sum_{n<N}(- 1)^{\nu(pn)}, \] where \(\nu(k)\) denotes the sum of the binary digits of \(k\) and \(p\) is a given odd number. After a recent account of the subject, the case \(p=17\) is studied in detail: the function \(S_{17}\) is shown to be always positive and its fractal nature is discussed. Then the authors use these sum-of-digits functions to generate a special code: the analysis of this code shows that it is exponential, extremely redundant and thus strongly error correcting with a linear decoding procedure.
Mathematics Subject Classification ID: 11A63
Mathematics Subject Classification ID: 94B35
Mathematics Subject Classification ID: 11Y55
Mathematics Subject Classification ID: 11B85
Mathematics Subject Classification ID: 11L07
zbMATH DE Number: 978146
zbMATH Keywords: Thue-Morse sequence
zbMATH Keywords: fractal digital sums
zbMATH Keywords: strongly error correcting codes
zbMATH Keywords: exponential sums
zbMATH Keywords: sum-of-digits functions
reviewed by: Valérie Berthé
MaRDI profile type: Publication
full work available at URL: s002000050050
OpenAlex ID: W1983631013
cites work: A summation formula related to the binary digits
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cites work: Character sum constructions of constrained error-correcting codes
cites work: On the Number of Binary Digits in a Multiple of Three
DOI: 10.1007/S002000050050
description: scientific article; zbMATH DE number 978146