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Motivated by the rank-modulation scheme with applications to flash memory, we consider Gray codes capable of detecting a single error, also known as snake-in-the-box codes. We study two error metrics: Kendall's $tau$-metric, which applies to charge-constrained errors, and the $ell_{infty}$-metric, which is useful in the case of limited-magnitude errors. In both cases, we construct snake-in-the-box codes with rate asymptotically tending to 1. We also provide efficient successor-calculation functions, as well as ranking and unranking functions. Finally, we also study bounds on the parameters of such codes.

 

 

 

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