Legendre pairs of lengths ℓ ≡ 0 (mod 5)

Abstract

By assuming a type of balance for length ℓ=87\ell =87 and nontrivial subgroups of multiplier groups of Legendre pairs (LPs) for length ℓ=85\ell =85, we find LPs of these lengths. We then study the power spectral density (PSD) values of mm compressions of LPs of length 5m5m. We also formulate a conjecture for LPs of lengths ℓ≡0\ell \equiv 0 (mod 5) and demonstrate how it can be used to decrease the search space and storage requirements for finding such LPs. The newly found LPs decrease the number of integers in the range ≤200\le 200 for which the existence question of LPs remains unsolved from 12 to 10.

Keywords

• compressed vector
• discrete fourier transform
• hadamard matrix
• periodic autocorrelation function
• power spectral density
• multiplier group
• 05b10
• 05b20
• 15b34