ON THE DECODING OF REED-SOLOMON AND BCH CODES OVER INTEGER RESIDUE RINGS

In this correspondence we present a decoding procedure for Reed-Solomo n (RS) and BCH codes defined over an integer residue ring pgZ(q), wher e q is a power of a prime p. The proposed decoding procedure, as for R S and BCH codes over fields, consists of four major steps: 1) calculat ion of the syndromes; 2) calculation of the ''elementary symmetric fun ctions,'' by a modified Berlekamp-Massey algorithm for commutative rin gs; 3) calculation of the error location numbers; and 4) calculation o f the error magnitudes. The proposed decoding procedure also applies t o the synthesis of a shortest linear-feedback shift register (LFSR), c apable of generating a prescribed finite sequence of elements lying in a commutative ring with identity.