2016/01/21 by Wang, Xiang, Fu, Fang-Wei
#FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.1601.05539
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 ℓ∞-metric are Gray codes, which can be capable of detecting one ℓ∞-error. In this paper, we give two constructions of ℓ∞-snakes. On the one hand, inspired by Yehezkeally and Schwartz's construction, we present a new construction of the ℓ∞-snake. The length of this ℓ∞-snake is longer than the length of the ℓ∞-snake constructed by Yehezkeally and Schwartz. On the other hand, we also give another construction of ℓ∞-snakes by using K-snakes and obtain the longer ℓ∞-snakes than the previously known ones.