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PreprintCC BY 4.0arXiv

Weight-constrained cut-down de Bruijn sequences

  • Chris J Mitchell
  • Peter R Wild
Open at sourcePDFDOICite

Abstract

In 2011/12, Ruskey, Sawada, Stevens and Williams showed that a binary cut-down de Bruijn sequence can be constructed containing all n-tuples of Hamming weight either r or r+1 for every possible r, and no others. In this paper we examine extensions of this result that require choosing a weight-like function applying to n-tuples with symbols taken from an alphabet of arbitrary (finite) size. We consider three possible such weight functions, and in each case establish an analogous result to that of Ruskey et al.

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Cite

BibTeXRIS
BibTeX
@misc{mitchell2026weightconstrained,
  title = {{Weight-constrained cut-down de Bruijn sequences}},
  author = {Chris J Mitchell and Peter R Wild},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2607.22350},
  eprint = {2607.22350},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.22350},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Weight-constrained cut-down de Bruijn sequences
AU  - Chris J Mitchell
AU  - Peter R Wild
PY  - 2026
DA  - 2026/10/16
PB  - arXiv
DO  - 10.48550/arxiv.2607.22350
UR  - https://arxiv.org/abs/2607.22350
AB  - In 2011/12, Ruskey, Sawada, Stevens and Williams showed that a binary cut-down de Bruijn sequence can be constructed containing all n-tuples of Hamming weight either r or r+1 for every possible r, and no others. In this paper we examine extensions of this result that require choosing a weight-like function applying to n-tuples with symbols taken from an alphabet of arbitrary (finite) size. We consider three possible such weight functions, and in each case establish an analogous result to that of Ruskey et al.
ER  -