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07.11.2019

# Snake-in-the-box codes under the $$\ell _{\infty }$$-metric for rank modulation

Zeitschrift:
Designs, Codes and Cryptography
Autoren:
Xiang Wang, Fang-Wei Fu
Wichtige Hinweise
Communicated by T. Etzion.

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## 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 some “push-to-the-top” operations. Moreover, snake-in-the-box codes under the $$\ell _{\infty }$$-metric ($$\ell _{\infty }$$-snakes) 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.

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