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PreprintCC BY 4.0arXiv

Conflict-avoiding codes and near-primitive roots

  • C. G. Karthick Babu
  • Pieter Moree
  • Sunil Kumar Pasupulati
  • Pietro Sgobba
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Abstract

An important role in the theory of conflict-avoiding codes is played by a quantity involving the multiplicative order of $4$ modulo d, with d running over all positive divisors of an odd integer n. We establish results on its distribution as n varies over the odd prime numbers, respectively odd integers, using techniques from the study of Artin's primitive root conjecture. We also point out some other interpretations of this quantity, with one of them making a connection with the factorization of Xnāˆ’1 into irreducibles over the finite field š”½2.

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Cite

BibTeXRIS
BibTeX
@misc{babu2026conflictavoiding,
  title = {{Conflict-avoiding codes and near-primitive roots}},
  author = {C. G. Karthick Babu and Pieter Moree and Sunil Kumar Pasupulati and Pietro Sgobba},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.05914},
  eprint = {2610.05914},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.05914},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Conflict-avoiding codes and near-primitive roots
AU  - C. G. Karthick Babu
AU  - Pieter Moree
AU  - Sunil Kumar Pasupulati
AU  - Pietro Sgobba
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2610.05914
UR  - https://arxiv.org/abs/2610.05914
AB  - An important role in the theory of conflict-avoiding codes is played by a quantity involving the multiplicative order of $4$ modulo d, with d running over all positive divisors of an odd integer n. We establish results on its distribution as n varies over the odd prime numbers, respectively odd integers, using techniques from the study of Artin's primitive root conjecture. We also point out some other interpretations of this quantity, with one of them making a connection with the factorization of X^nāˆ’1 into irreducibles over the finite field š”½_2.
ER  -