Introduction to finite fields and their applications
Introduction to finite fields and their applications
Algebraic decoding of the (23,12,7) Golay code
IEEE Transactions on Information Theory
Decoding the (47,24,11) quadratic residue code
IEEE Transactions on Information Theory
General Error Locator Polynomials for Binary Cyclic Codes With and
IEEE Transactions on Information Theory
Algebraic Decoding of the Quadratic Residue Code
IEEE Transactions on Information Theory
Unusual general error locator polynomial for the (23, 12, 7) golay Code
IEEE Communications Letters
Decoding binary cyclic codes with irreducible generator polynomials up to actual minimum distance
IEEE Communications Letters
Hi-index | 754.84 |
In this paper, three algebraic decoding algorithms are proposed for the binary quadratic residue (QR) codes generated by irreducible polynomials. The polynomial relations among the syndromes and the coefficients of the error-locator polynomials have been computed with Lagrange interpolation formula (LIF). Unlike some previous QR decoders, which may take several iterations to decode a corrupted word, the iteration number of the first two algorithms is at most one. The processes in the first algorithm are the calculation of consecutive syndromes, inverse-free Berlekamp-Massey algorithm (IFBMA), and the Chien search. One of Orsini-Sala's results on the structure of general error-locator polynomials is generalized and applied to derive the second (respectively, third) algorithm that consists of the determination of general error-locator polynomial (respectively, classical error-locator polynomials) and the Chien search. Finally, the (17,9,5), (23,12,7) and (41,21,9) QR decoders are illustrated and their complexity analyses are given.