How to produce quadruple density wavelet coefficients in Matlab?

I refer to this paper , second-page right-column second-paragraph, where it is stated how to produce quadruple density wavelet coefficients.

"if we do not down sample the wavelet coefficients we generate wavelets with double density, where wavelets of level n are centered every 1/2*2^n. To generate the quadruple density dictionary,we compute the scaling coefficients with double density by not down sampling them. The next step is to calculate double density wavelet coefficients on the two sets of scaling coefficients - even and odd - separately."

I am confused how to get two sets of scaling coefficients - even and odd. What does it mean by even and odd?

How can I compute quadruple density wavelet transform in Matlab?

Thanks