2022/12/21 by Ilias Kotsireas, Kotsireas, Ilias S., Arne Winterhof +1
Engineering · #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2212.10953
openalex publication_date 2022/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce quaternary Legendre pairs of length ℓ. In contrast to binary Legendre pairs they can exist for even ℓ as well. First we show that they are pertinent to the construction of quaternary Hadamard matrices of order 2ℓ+2 and thus of binary Hadamard matrices of order 4ℓ+4. Then for a prime p>2 we present a construction of a pair of sequences of length p from which we can derive quaternary Legendre pairs of length ℓ=2p by decompression for p=3,5,7,13,19,31,41. Moreover, we give also constructions of Legendre pairs of length ℓ for all remaining even ℓ≤ 24.