Search results for "Constant-weight code"
showing 5 items of 5 documents
Gray code for permutations with a fixed number of cycles
2007
AbstractWe give the first Gray code for the set of n-length permutations with a given number of cycles. In this code, each permutation is transformed into its successor by a product with a cycle of length three, which is optimal. If we represent each permutation by its transposition array then the obtained list still remains a Gray code and this allows us to construct a constant amortized time (CAT) algorithm for generating these codes. Also, Gray code and generating algorithm for n-length permutations with fixed number of left-to-right minima are discussed.
An optimal code for patient identifiers.
2004
How to distinguish 1 billion individuals by an identifier consisting of eight characters, allowing a reasonable amount of error detection or even error correction? Our solution of this problem is an optimal code over a 32-character alphabet that detects up to two errors and corrects one error as well as a transposition of two adjacent characters. The corresponding encoding and error checking algorithms are available for free; they are also embedded as components of the pseudonymisation service that is used in the TMF-the German telematics platform for health research networks.
Quantum error correction and detection: Quantitative analysis of a coherent-state amplitude-damping code
2013
We re-examine a non-Gaussian quantum error correction code designed to protect optical coherent-state qubits against errors due to an amplitude damping channel. We improve on a previous result [Phys. Rev. A 81, 062344 (2010)] by providing a tighter upper bound on the performance attained when considering realistic assumptions which constrain the operation of the gates employed in the scheme. The quantitative characterization is performed through measures of fidelity and concurrence, the latter obtained by employing the code as an entanglement distillation protocol. We find that, when running the code in fully-deterministic error correction mode, direct transmission can only be beaten for ce…
Diagonal space time hadamard codes with erasure decoding algorithm
2005
A major challenge in the area of space time (ST) codes is to find codes suitable for efficient decoding, thus overcoming the problem of many existing ST code designs which require maximum-likelihood (ML) decoding. A solution could be to apply single-input single-output (SISO) channel codes and theory over temporal channel fading to the multi-input single-output (MISO) code construction and classical suboptimum decoding methods. For these purposes, an ST code construction which allows the use of efficient decoding algorithms is described. We propose a concatenated code, where the inner code is the diagonal ST Hadamard (D-STH) code with Paley constructions and the outer code is an algebraic b…
On strongly tactical codes
1986
We study perfect error correcting codes in which the codewords are protected by Hamming spheres of distinct protective radii. These codes have been introduced by Cohen, Montaron and Frankl [3, 4, 10].