Legendre pairs of lengthsℓ≡ 0 (mod 5)

Abstract

AbstractBy assuming a type of balance for lengthℓ=87\ell =87and nontrivial subgroups of multiplier groups of Legendre pairs (LPs) for lengthℓ=85\ell =85, we find LPs of these lengths. We then study the power spectral density (PSD) values ofmmcompressions of LPs of length5m5m. We also formulate a conjecture for LPs of lengthsℓ≡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 200for which the existence question of LPs remains unsolved from 12 to 10.