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Applicable Algebra in Engineering Communication and Computing
Article . 1997 . Peer-reviewed
License: Springer TDM
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Article . 2022
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Universal Sequences

Universal sequences
Authors: Henk D. L. Hollmann; Jacobus H. van Lint;

Universal Sequences

Abstract

Untersucht wird wie lang mindestens eine \((0,1)\)-Test-Folge sein muß, um darin für jedes \(m\) (mit \(k\leq m\leq n\) bei vorgegebenen \(k,n)\) mit \(2^{k}\) Teilfolgen davon alle \((0,1)\)-Folgen der Länge \(k\) zu erhalten, wobei die Teilfolgen spätestens mit dem jeweils \(m\)-ten Folge-Element der Test-Folge vom Teilfolgen-Beginn an endet. Offensichtlich ist die Test-Folgen-Länge bei \(k=n\) mindestens \(2^{k+ (n-1)}\), bei Kreis-Folgen \(2^k\); es gilt sogar Gleichheit wegen Existenz der DeBruijn-Folgen. Für verschiedene Einschränkungen werden Abschätzungen gegeben, insbesondere für \(m=n\). Mit Hilfe von Euler's varphi-Funktion wird auch gezeigt, daß sich Kreis-Testfolgen für \(n\) = Primzahl leicht daraus ableiten lassen.

Country
Netherlands
Related Organizations
Keywords

Other combinatorial number theory, Shift register sequences and sequences over finite alphabets in information and communication theory, \((0,1)\)-test sequences, subsequences, test sequence length, universal sequences, VLSI-testing, Fault detection; testing in circuits and networks, circle sequences

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average
bronze