Limited-Magnitude Error-Correcting Gray Codes for Rank Modulation

We construct Gray codes over permutations for the rank-modulation scheme, which are also capable of correcting errors under the infinity - metric. These errors model limited - magnitude or spike errors, for which only single-error-detecting Gray codes are currently known. Surprisingly, the error-correcting codes we construct achieve better asymptotic rates than that of presently-known constructions not having the Gray property. We also cast the problem of improving upon these results into the context of finding a certain type of auxiliary codes in the symmetric group of even orders.