Designs, Codes and Cryptography

, Volume 85, Issue 3, pp 483–521 | Cite as

Consolidation for compact constraints and Kendall tau LP decodable permutation codes

Article

Abstract

Invented in the 1960s, permutation codes have reemerged in recent years as a topic of great interest because of properties making them attractive for certain modern technological applications, especially flash memory. In 2011 a polynomial time algorithm called linear programming (LP) decoding was introduced for a class of permutation codes where the feasible set of codewords was a subset of the vertex set of a code polytope. In this paper we investigate a new class of linear constraints for matrix polytopes with no fractional vertices through a new concept called “consolidation.” We then introduce a necessary and sufficient condition for which LP decoding methods, originally designed for the Euclidean metric, may be extended to provide an efficient decoding algorithm for permutation codes with the Kendall tau metric.

Keywords

Coding and information theory Graphs and abstract algebra Linear programming Permutation groups Decoding 

Mathematics Subject Classification

68P30 05C25 90C05 20B 94B35 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Mathematics and InformaticsChiba UniversityChiba CityJapan

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