Omega: a system for the effective construction, coding and decoding of block error-correcting codes Authors Sebastià Xambó i Descamps Abstract In this work, we show how to implement effective constructions, coding and decoding of algebraic codes by means of Omega, a system specifically designed and programmed for general mathematical computations. For alternant codes, the main class we consider (which includes BCH, RS and classical Goppa codes), we give an implementation of the Euclidean division BM decoding algorithm. For cyclic codes we implement the Meggitt decoder, and to illustrate how it works we provide an implementation of the Meggitt syndrome tables for the two Golay codes. Finally, we present several other groups of functions and the computations and problems (still almost in the area of error-correcting codes) they solve. Downloads Text complet Published 2001-06-08 Issue 1-2 Section Focus License This work is subject, unless the contrary is indicated in the text, the photographs or in other illustrations, to an Attribution —Non-Commercial— No Derivative Works 3.0 Creative Commons License, the full text of which can be consulted at http://creativecommons.org/licenses/by-nc-nd/3.0/. You are free to share, copy, distribute and transmit the work provided that the author is credited and reuse of the material is restricted to non-commercial purposes only and that no derivative works are created from the original material.
