Concatenated Permutation Codes under Chebyshev Distance

Serially Concatenated Convolutional Codes with Product Distance

J. Freudenberger*, R. Jordan*, M. Bossert*, and S. Shavgulidze** * University of Ulm, Dep. of Information Technology Albert-Einstein-Allee 43, D-89081 Ulm, Germany Email: jfreuden,jordan,[email protected] ** Georgian Technical University, Dep. of Digital Communication Theory Kostava str. 77, Tbilisi 380075, Georgia Email: sergo [email protected] Abstract: In this paper we investigate s...

Permutation codes invariant under isometries

The symmetric group Sn on n letters is a metric space with respect to the Hamming distance. The corresponding isometry group is well known to be isomorphic to the wreath product Sn oS2. A subset of Sn is called a permutation code or a permutation array, and the largest possible size of a permutation code with minimum Hamming distance d is denoted by M(n, d). Using exhaustive search by computer ...

Concatenated codes

Quantum accuracy threshold for concatenated distance-3 codes

We prove a new version of the quantum threshold theorem that applies to concatenation of a quantum code that corrects only one error, and we use this theorem to derive a rigorous lower bound on the quantum accuracy threshold ε0. Our proof also applies to concatenation of higher-distance codes, and to noise models that allow faults to be correlated in space and in time. The proof uses new criter...

Proof of a conjecture of Kløve on permutation codes under the Chebychev distance

Let d be a positive integer and x a real number. Let Ad,x be a d× 2d matrix with its entries ai,j = 