Construction and decoding of BCH codes over finite commutative rings

Linear Algebra and Its Applications

Volumn 286, Issue 1-3, 1999, Pages 69-85

  De Andrade, Antonio Aparecido ^a   Palazzo Jr , Reginaldo ^b  

^a SÃO PAULO STATE UNIVERSITY UNESP   (Brazil)

^b UNIVERSITY OF CAMPINAS   (Brazil)

Author keywords

BCH codes; Error location numbers; Forney's method; Galois extension; Modified Berlekamp Massey algorithm; Syndrome calculation

Indexed keywords

EID: 0039627876     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(98)10163-5     Document Type: Article

References (11)

1. 4 -linearity of Kerdock, Preparata, Goethals and related codes, IEEE Trans. Inform. Theory IT-40 (1994) 301-319.
2. 2-linear binary codes, k > 2, II Pan-American Workshop in Applied Mathematics, Gramado, Brazil, September 7-12, 1997.
3. P. Shankar, On BCH codes over arbitrary integer rings, IEEE Trans. Inform. Theory IT-25 (1979)480-483.
4. J.C. Interlando, R. Palazzo, Jr., M. Elia, On the decoding of Reed-Solomon and BCH codes over integer residue rings, IEEE Trans. Inform. Theory IT-43 (1997) 1013-1021.
5. J.A. Reeds, N.J.A. Sloane, Shift register synthesis (mod m), SIAM J. Computing 14 (1985) 505-513.
6. B.R. McDonald, Finite Rings with Identity, Marcel Dekker, New York, 1974.
7. A.A. Andrade, R. Palazzo Jr., A Note on Units of a Local Finite Rings, submitted for publication.
8. W.W. Peterson, E.J. Weldon Jr., Error Correcting Codes, 2nd ed., MIT Press, Cambridge, MA, 1972.
9. I.N. Herstein, Topics in Algebra, Wiley, New York, 1975.
10. A.A. Andrade, R. Palazzo Jr., Linear Block Codes over Finite Commutative Rings with identity, to appear by Rev. Mat. Estat., São Paulo, Brazil, in portuguese.
11. G.D. Forney, Jr., On decoding BCH codes, IEEE Trans. Inform. Theory IT-11 (1965) 549-557.