Technical Program

Paper Detail

Paper Title Permutation Code Equivalence is Not Harder Than Graph Isomorphism When Hulls Are Trivial
Paper IdentifierTH4.R9.4
Authors Magali Bardet, Ayoub Otmani, LITIS, University of Rouen Normandie, France; Mohamed Saeed-Taha, University of Khartoum, Sudan
Session Computational Complexity
Location Pontoise, Level 5
Session Time Thursday, 11 July, 16:40 - 18:00
Presentation Time Thursday, 11 July, 17:40 - 18:00
Manuscript  Click here to download the manuscript
Abstract The paper deals with the problem of deciding if two finite-dimensional linear subspaces over an arbitrary field are identical up to a permutation of the coordinates. This problem is referred to as the permutation code equivalence. We show that given access to a subroutine that decides if two weighted undirected graphs are isomorphic, one may deterministically decide the permutation code equivalence provided that the underlying vector spaces intersect trivially with their orthogonal complement with respect to an arbitrary inner product. Such a class of vector spaces is usually called linear codes with trivial hulls. The reduction is efficient because it essentially boils down to computing the inverse of a square matrix of order the length of the involved codes. Experimental results obtained with randomly drawn binary codes having trivial hulls show that permutation code equivalence can be decided in a few minutes for lengths up to 50,000.