Decoding binary cyclic codes with irreducible generator polynomials up to actual minimum distance

Authors:
Chong-Dao Lee;Yaotsu Chang;Ming-Haw Jing;Jian-Hong Chen
Affiliations:
Departments of Communication Engineering, Applied Mathematics, Information Engineering, and Information Engineering, I-Shou University, Kaohsiung County, Taiwan, R.O.C.;Departments of Communication Engineering, Applied Mathematics, Information Engineering, and Information Engineering, I-Shou University, Kaohsiung County, Taiwan, R.O.C.;Departments of Communication Engineering, Applied Mathematics, Information Engineering, and Information Engineering, I-Shou University, Kaohsiung County, Taiwan, R.O.C.;Departments of Communication Engineering, Applied Mathematics, Information Engineering, and Information Engineering, I-Shou University, Kaohsiung County, Taiwan, R.O.C.
Venue:
IEEE Communications Letters
Year:
2010

Citing 6
Cited 0

Introduction to finite fields and their applications

Introduction to finite fields and their applications
On the decoding of binary cyclic codes with the Newton identities

Journal of Symbolic Computation
Algebraic decoding of a class of binary cyclic codes via Lagrange interpolation formula

IEEE Transactions on Information Theory
Unusual general error locator polynomial for the (23, 12, 7) golay Code

IEEE Communications Letters
Finite Fields And Galois Rings

Finite Fields And Galois Rings
General Error Locator Polynomials for Binary Cyclic Codes With and

IEEE Transactions on Information Theory

Quantified Score

Hi-index	0.00

Visualization

Abstract

This letter presents two modified algorithms to decode up to actual minimum distance for binary cyclic codes with irreducible generator polynomials. The key ideas behind these decoding algorithms are the utilization of the extended Euclid's algorithm for univariate polynomials to evaluate the unknown syndromes and the coefficients of general error locator polynomial, which has not been developed before. The advantage of these algorithms is particularly suitable for software and hardware implementations.