Code word components erroneous aggregates locating method for decoder, involves regrouping polynomials in one variable of word with monomials of another variable to define matrix whose determinant is polynomial nullified on former variable

摘要

The method involves determining a Grobner base associated to a received code word and comprising polynomials (Fi(X,Y)), and determining polynomials (Ys>.Fi(X,Y)), each being a product of a polynomial (Fi(X,Y)) and a power (Ys>) of the variable (Y), to obtain, by addition with the base, an extended set of polynomials. Polynomials (phi (i,j)(X)) in the variable (X) are regrouped with monomials of the variable (Y) to define a polynomial matrix whose determinant is a polynomial which is nullified on a coordinate (x) of erroneous points (x,y) of the word. Independent claims are also included for the following: (1) a method for decoding a received word (2) a coded digital signal receiving apparatus comprising a decoder having an error location device (3) a computing system comprising a decoder (4) a data storage medium comprising computer program code instructions for executing a word components erroneous aggregates locating method (5) a computer program, containing instructions to implement a word components erroneous aggregates locating method.