Titlebook: ;

树木心

Decoding Cyclic Codes: the Cooper PhilosophyIn 1990 Cooper suggested to use Gröbner basis computations in order to deduce error locator polynomials of cyclic codes..The aim of this tutorial is to show, with illuminating examples, how Cooper’s approach has been refined up to give both an . and ..

脆弱吧

Algebraic Geometry Codes from Order DomainsIn this tutorial we introduce order domains and study the related codes. Special attention is given to the one-point geometric Goppa codes. We show how Gröbner basis theory helps us constructing order domains as well as helps us dealing with the related codes.

婴儿

A Tutorial on AG Code Decoding from a Gröbner Basis PerspectiveThis chapter presents material about syndrome decoding and list decoding of AG codes. The syndrome decoding of AG codes is viewed in terms of Sakata’s generalization of the Berlekamp–Massey algorithm and Feng and Rao’s majority voting scheme. Their list-decoding is viewed following Sudan’s ideas and some variations.

压倒性胜利

Overview of Cryptanalysis Techniques in Multivariate Public Key CryptographyThis paper summarizes most of the main developments in the cryptanalysis of multivariate cryptosystems and discuss some problems that remain open. A strong emphasis is put on the symbolic computation tools that have been used to achieve these advances.

inculpate

An Introduction to Linear and Cyclic Codeson. To do this we introduce, with examples, the concept of linear codes and their parameters, in particular the Hamming distance..A fundamental subclass of linear codes is given by cyclic codes, that enjoy a very interesting algebraic structure. In fact, cyclic codes can be viewed as ideals in a res

PLAYS

母猪

躲债

The BMS Algorithm (1) How is it related to Gröbner basis? (2) What problem can it solve? (3) How does it work? (4) Its variations. First we discuss another problem closely related to our main problem, and introduce some concepts about .-D linear recurrences and modules of .-D arrays as their general solutions. These

混乱生活

The BMS Algorithm and Decoding of AG CodesHøholdt et al. in Handbook of coding theory, vols. I, II, North-Holland, Amsterdam, pp. 871–961, .; Geil in Algebraic geometry codes from order domains, this volume, pp. 121–141, .) mainly based on the Gröbner basis theory (Buchberger in Ein Algorithmus zum Auffinden der Basiselemente des Restklasse

conformity