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On the decoding of Reed-Solomon and BCH codes over integer residue rings

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3 Author(s)
Interlando, J.C. ; Dept. of Commun., Univ. Estadual de Campinas, Sao Paulo, Brazil ; Palazzo, R., Jr. ; Elia, M.

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

Published in:

Information Theory, IEEE Transactions on  (Volume:43 ,  Issue: 3 )

Date of Publication:

May 1997

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