On the exact size of maximum impulse radio sequences with parameters (m,k,λ,k−1)(m,k,λ,k−1)

Impulse radio sequences (IRSs) were introduced by Chu and Colbourn to study sequence or signal design for ultrawideband radio with unmodulated time-hopping. The central researches on IRSs lie in the determination of the value Ψ(m,k,λa,λc)Ψ(m,k,λa,λc), i.e., the largest possible number of sequences in an (m,k,λa,λc)(m,k,λa,λc)-IRS. When λa=λc=k−1λa=λc=k−1, Chang and Wang have determined the value of Ψ(m,k,k−1,k−1)Ψ(m,k,k−1,k−1). As far as the authors know, there has been no study on the case of λa≠λcλa≠λc. So we in this paper focus on this case with λc=k−1λc=k−1. We will determine the exact value of Ψ(m,k,k,k−1)Ψ(m,k,k,k−1) for any positive integers mm and kk. We also calculate the exact value of Ψ(m,k,λ,k−1)Ψ(m,k,λ,k−1) for k=3,4k=3,4 and 1≤λ≤k−21≤λ≤k−2.