Method for performing error corrections of digital information codified as a symbol sequence
A method and system for making error corrections on digital information coded as symbol sequences, for example digital information stored in electronic memory systems or transmitted from and to these systems is described, provides the transmission of sequences incorporating a portion of error corrector code allowing the sequence which is more probably the original transmitted through the calculation of an error syndrome using a parity matrix to be restored when received. Advantageously according to embodiments of the invention, the error code incorporated in the original sequence belongs to a non Boolean group.
1. A method for making error corrections on digital information coded as symbol sequences, the method comprising:
providing the transmission of sequences incorporating a portion of an error corrector code which allows the sequence which is more probably the original transmitted through the calculation of an error syndrome using a parity matrix to be restored when received;
wherein the error corrector code incorporated in the original sequence belongs to a non Boolean group;
wherein said parity matrix comprises an identity matrix having a non-zero determinant;
wherein each number belonging to the parity matrix is not a linear combination of other numbers belonging to the same matrix;
wherein operating in a group (mod p), a parity bit number n−k is fixed and p is chosen so that (2 n−k +1)≦ p≦2 n−k+1 −1;
wherein n equals a total number of bits in each sequence; and
wherein k equals the number of information bits forming the digital information.
2. A method according to claim 1 , wherein said error corrector code belongs to an Abelian group.
3. A method according to claim 1 , wherein said error corrector code is a code in systematic form.
4. The method of claim 1 wherein the digital information comprises digital information stored in electronic memory systems or transmitted from and to these system.
5. A method according to claim 4 , wherein said error corrector code is a linear code.
6. A method according to claim 4 , wherein said error corrector code recognizes an error of the 0→1 type from an error of the 1→0 type.