I watched Persi give a talk where he demonstrated this trick, as part of a lecture on ways to use finite field theory to find de Bruijn sequences.

I hadn't seen Persi in a while; we'd written the "seven shuffles" paper together. Catching up, I asked him privately afterwards why he didn't use a sequence where two bits encoded the suit, then three bits encoded the card. He grinned wildly, then pulled out a spare deck to establish this was indeed what he had actually done. The spare deck was wrong. He joked how he dodged a bullet not using that deck.

That evening I burst out laughing in a solemn moment of an earnest modern dance performance. This was embarrassing, to say the least. I had recalled that Persi had shuffled the deck once as part of his demonstration of the trick. He's a legendary magician one rarely sees performing. Perfect shuffles were easy for him.