โ Scribed by R.M. Campello de Souza; P.G. Farrell
No coin nor oath required. For personal study only.
methods for error-correcting codes which are based on syndrome look-up tables are of limited use due to the rapidly increasing amount of storage that they require as the number of check digits of the code increases.
A method is described which uses shortened syndrome look-up tables in an efficient way, thus providing an improvement with respect to classical syndrome decoding methods. The algorithm can be characterised in general as a type of permutation decoding which uses transform domain information, with the interesting variation that permutations not preserving the code are also allowed.
* Presented at the International Symposium on Algebra and Error Correcting Codes: Theory and Applications,
๐ SIMILAR VOLUMES
Let F be a finite field. We apply a result of Thierry Berger (1996, Designs Codes Cryptography, 7, 215-221) to determine the structure of all groups of permutations on F generated by the permutations induced by the linear polynomials and any power map which induces a permutation on F.