Constructions of Snake-in-the-Box Codes under ${\ell }_{\infty }$-metric for Rank Modulation

Abstract

In the rank modulation scheme, Gray codes are very useful in the realization of flash memories. For a Gray code in this scheme, two adjacent codewords are obtained by using one "push-to-the-top" operation. Moreover, snake-in-the-box codes under the ${\ell }_{\infty }$-metric are Gray codes, which can be capable of detecting one ${\ell }_{\infty }$-error. In this paper, we give two constructions of ${\ell }_{\infty }$-snakes. On the one hand, inspired by Yehezkeally and Schwartz's construction, we present a new construction of the ${\ell }_{\infty }$-snake. The length of this ${\ell }_{\infty }$-snake is longer than the length of the ${\ell }_{\infty }$-snake constructed by Yehezkeally and Schwartz. On the other hand, we also give another construction of ${\ell }_{\infty }$-snakes by using $\mathcal{K}$-snakes and obtain the longer ${\ell }_{\infty }$-snakes than the previously known ones.

Cited by in corpus (2)

• Limited-Magnitude Error-Correcting Gray Codes for Rank Modulation
• Infinity-Norm Permutation Covering Codes from Cyclic Groups