T-Walsh has for some unknown reason (to me anyway), internationally, become the name for transfer responses to 1C (natural/balanced).
This transfer treatment to 1C was likely developed independently in various parts of the world. In Sweden Nilsland/Wirgren/Lindkvist, "the Scanians", developed it in the mid-80's. Nilsland-Wirgren played it in their highly sophisticated system Super Standard (collecting bronze in Rosenblum 1986). This system was published in a book 1990 (still available as e-book from Scania Bridgekonsult).
The question today is how you should defend in 4th position after 1C - pass - 1D/H - ? There is no clear 'standard way' or established 'best practises' but here is my prefered defence:
X = general strength, doesn't promise length in other suits, typically balanced or strong unbalanced. Next X is T/O from both, a subsequent 3rd X is penalty from both regardless.
1-lvl cue = 8+hcp, 4-card other major & 5+minor. Lowest club-bid is pass/corret, NT-bid asks for long minor.
1NT = constructive overcall in bid suit: 1C - p - 1D - 1NT = 5+D or 1C - p - 1H - 1NT = 5+H (also works for 1C - p - 1S - 1NT = 5+S).
"cue" = ca 9-13 hcp w/6+suit, natural: 1C - p - 1D - 2D or 1C - p - 1H - 2H.
2-lvl cue = ca 12-16 hcp w/6+suit, natural in shown suit: 1C - p - 1D - 2H or 1C - p - 1H - 2S.
As always as long as you have an agreement, you´re ok most of the time.