2015/06/09 by Yiwei Zhang, Gennian Ge, Zhang, Yiwei +1
Computer Science · Engineering · #Cellular Automata and Applications #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1506.02740
openalex publication_date 2015/06/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
For a Gray code in the scheme of rank modulation for flash memories, the codewords are permutations and two consecutive codewords are obtained using a push-to-the-top operation. We consider snake-in-the-box codes under Kendall's τ-metric, which is a Gray code capable of detecting one Kendall's τ-error. We answer two open problems posed by Horovitz and Etzion. Firstly, we prove the validity of a construction given by them, resulting in a snake of size M2n+1=((2n+1)!)/(2)-2n+1. Secondly, we come up with a different construction aiming at a longer snake of size M2n+1=((2n+1)!)/(2)-2n+3. The construction is applied successfully to S7.