2012/02/01 by Fabian Lim, Lim, Fabian, Manabu Hagiwara +1
Computer Science · Engineering · #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1202.0241
openalex publication_date 2012/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recent interest on permutation rank modulation shows the Kendall tau metric as an important distance metric. This note documents our first efforts to obtain upper bounds on optimal code sizes (for said metric) ala Delsarte's approach. For the Hamming metric, Delsarte's seminal work on powerful linear programming (LP) bounds have been extended to permutation codes, via association scheme theory. For the Kendall tau metric, the same extension needs the more general theory of coherent configurations, whereby the optimal code size problem can be formulated as an extremely huge semidefinite programming (SDP) problem. Inspired by recent algebraic techniques for solving SDP's, we consider the dual problem, and propose an LP to search over a subset of dual feasible solutions. We obtain modest improvement over a recent Singleton bound due to Barg and Mazumdar. We regard this work as a starting point, towards fully exploiting the power of Delsarte's method, which are known to give some of the best bounds in the context of binary codes.