Three new lengths for cyclic Legendre pairs
N. A. Balonin, D. \v{Z}. {\DJ}okovi\'c
TL;DR
This paper reports the construction of Legendre pairs for lengths 91, 93, and 123, significantly reducing the number of undecided cases among odd integers less than 200.
Contribution
It introduces new Legendre pairs for three specific lengths, advancing the understanding of their existence for certain odd integers.
Findings
Legendre pairs constructed for lengths 91, 93, and 123
Number of undecided cases reduced from 20 to 17
Provides new examples for lengths previously unresolved
Abstract
There are 20 odd integers v less than 200 for which the existence of Legendre pairs of length v is undecided. The smallest among them is v=77. We have constructed Legendre pairs of lengths 91, 93 and 123 reducing the number of undecided cases to 17.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
Topicsgraph theory and CDMA systems · Algorithms and Data Compression · Cellular Automata and Applications