14 research outputs found
Fourier transform over finite groups for error detection and error correction in computation channels
We consider the methods of error detection and correction in devices and programs calculating functions f: G → K where G is a finite group and K is a field. For error detection and correction we use linear checks generated by convolutions in the field K of the original function f and some checking idempotent function δ: G → , 1 For the construction of the optimal checking function δ we use methods of harmonic analysis over the group G in the field K. Since these methods will be the main tools for the construction of optimal checks, we consider the algorithms for the fast computation of Fourier Transforms over the group G in the field K. We solve the problem of error detecting and correcting capability for our methods for two important classes of decoding procedures (memoryless and memory-aided decoding) and consider the question of syndrome computation for these methods. We describe also properties of error correcting codes generated by convolution checks
Characterizing extremal digraphs for identifying codes and extremal cases of Bondy's theorem on induced subsets
An identifying code of a (di)graph is a dominating subset of the
vertices of such that all distinct vertices of have distinct
(in)neighbourhoods within . In this paper, we classify all finite digraphs
which only admit their whole vertex set in any identifying code. We also
classify all such infinite oriented graphs. Furthermore, by relating this
concept to a well known theorem of A. Bondy on set systems we classify the
extremal cases for this theorem