I'm sorry but that doesn't make much sense to me, firstly because it's not clear what you mean in part b): What is left/right? Linear/rotated with respect to what? And that's not the terminology is Castro's books anyway.
Thanks everyone (newbie, andabien, ukdancer) for your replies. Sorry it's late here 1.30am so only a quick reply to try to explain what I meant on the first bit before heading to bed.
In terms of steps (in Borisvan's abbreviations, post 26) in a couple we can either step O/O, O/C, C/O or C/C.
Reading the book, as well as saying these were the only basic movements, it also seemed to be describing an equivalence between these steps and movements in a drawn out way.
If the starting point is fixed so we've already decided which legs we're standing on, then the system is fixed. So say I'm on my left foot and my follower is on her right foot, then we're in parallel leg system. Then
O/O we must take a 'linear' step to my 'right'.
O/C we must 'rotate' to the leaders 'left'
C/O we must 'rotate' to the leaders 'right'
C/C we must take a 'linear' step to the leaders left.
In my terminology I take 'left' and 'right' to mean to the leaders left and to the leader's right. (I think Castro does use L and R in a similar way when referring to one person moving wrt the other). Linear and rotated to mean a step where we are not rotating or we are rotating. Castro I think uses 'Parallel' and 'Contrary' directions respectively. So (left/rotated) is an anticlockwise turn, (left/linear) is a left step
But I guess my point is that this can be turned around. So
(Linear/Right) means we must take the O/O step
(Rotate/Left) means we must take the O/C step
(Rotate/Right) means we must take the C/O step
(Linear/Left) means we must take the C/C step
So they are an equivalence. And it's because moving to my right I have to take an open step and to the left a closed step (in this example starting position)
And that it would be useful because it's easier to think in movements than in O/C steps. So at each point we can only structurally take a (linear) step to our left, a step to our right, a clockwise turn or an anticlockwise turn and this fully describes all the steps we can take as a couple.
Anyway I hope that explains what my thought process was - but I'm not sure whether it's too simplistic or whether it's what Castro was describing? Have I completely missed the point? Borisvan, it seems that this is similar to what you were saying in your post 26, but not sure if it's the same?