On Minimal Realization Over a Finite Chain Ring
Designs, Codes and Cryptography
On the Key Equation Over a Commutative Ring
Designs, Codes and Cryptography
Algorithms for computing parameters of graph-based extensions of BCH codes
Journal of Discrete Algorithms
| Hi-index | 754.84 |
We present a decoding procedure for Reed-Solomon (RS) and BCH codes defined over an integer residue ring pgZq, where q is a power of a prime p. The proposed decoding procedure, as for RS and BCH codes over fields, consists of four major steps: (1) calculation of the syndromes; (2) calculation of the “elementary symmetric functions,” by a modified Berlekamp-Massey (1968, 1969) algorithm for commutative rings; (3) calculation of the error location numbers; and (4) calculation of the error magnitudes. The proposed decoding procedure also applies to the synthesis of a shortest linear-feedback shift register (LFSR), capable of generating a prescribed finite sequence of elements lying in a commutative ring with identity