Group Geometries and Error-Correcting Codes

Group Homomorphisms as Error Correcting Codes

We investigate the minimum distance of the error correcting code formed by the homomorphisms between two finite groups G and H. We prove some general structural results on how the distance behaves with respect to natural group operations, such as passing to subgroups and quotients, and taking products. Our main result is a general formula for the distance when G is solvable or H is nilpotent, i...

18.S096: Group Testing and Error-Correcting Codes

During the Second World War the United States was interested in weeding out all syphilitic soldiers called up for the army. However, syphilis testing back then was expensive and testing every soldier individually would have been very costly and inefficient. A basic breakdown of a test is: 1) Draw sample from a given individual, 2) Perform required tests, and 3) Determine presence or absence of ...

Synchronizable Error-Correcting Codes

A new technique for correcting synchronization errors in the transmission of discrete-symbol information is developed. The technique can be applied to any t-additive-error-correcting Bose-Chaudhuri-Hocquenghem code, to provide protection against synchronization errors. The synchronization error is corrected at the first complete received word after the word containing the synchronization error,...

Parallel error correcting codes

Error-Correcting Codes

Transmission of information takes place over “noisy” signals. This is the case in satellite transmissions and storing data. For this reason, it is useful to encode information so that errors can be detected and corrected. For our purposes, we will assume all information to be encoded constists of words of fixed length k using symbols from a fixed alphabet, and all encoded messages are divided i...