In this question orthogonal family and pulse shaping filter the user asked about possible loss of orthogonality of orthogonal codes due to the use of raised cosine pulse shaping and I showed as an answer how a correlation between codes can occur due to pulse shaping.
This leads me to the question of orthogonal codes for use in band limited channels. Are there such codes that exist that both provide band limiting (similar to what raised-cosine pulse shaping provides) and guarantee complete orthogonality between the band limited waveforms themselves? Here orthogonal means the inner product (dot product) between the waveforms is zero.
In particular as a matter of technical interest I am interested in solutions that mathematically result in 0 (such as Walsh codes prior to any pulse shaping when properly synchronized). If this does not exist then the solution that provides a complete family of codes and has the lowest relative cross correlation (relative to other solutions of the same code size) will be selected as the best answer. As I found in the linked question, testing just two samples of the complete code family are not sufficient to conclude.