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International Symposium on Coding Theory and Applications (held in Europe)

EUROCODE 1990: EUROCODE '90 pp 6–20Cite as

A note on automorphism groups of codes and symbol error probability computation

  • Section 1 Algebraic Codes
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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 514))

Abstract

In this paper we consider code automorphism groups and their effects on the computation of the symbol error probability after complete decoding. In particular both Maximum Likelihood and Unique Coset Leader decoding strategies are investigated when applied to Reed-Solomon codes. Therefore referring to these codes several explicit formulas for the evaluation of the symbol error probability are obtained.

His work was financially supported by the Italian CNR (Consiglio Nazionale delle Ricerche) under grant n. 87.02717.07.

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References

  1. F.J. MacWilliams and N.J.A. Sloane, The Theory of Error Correcting Codes, Elsevier, New York, 1976.

    Google Scholar 

  2. A.M. Michelson and A.H. Levesque, Error-Control Techniques for Digital Communication, Wiley, New York, 1985.

    Google Scholar 

  3. V. Pless, The Theory of Error Correcting Codes, Wiley, New York, 1989.

    Google Scholar 

  4. S. Benedetto, M. Elia and G. Taricco On Symbol Error Probability Computation for Reed-Solomon Codes, submitted to IEEE Trans. on Inform. Theory.

    Google Scholar 

  5. G.D. Cohen, M.G. Karpovsky, H.F. Mattson Jr., and J.R. Schatz, Covering radius: A survey and recent results, IEEE Trans. on Inform. Theory, vol.IT-31, no. 3, May 1985, pp. 328–343.

    Article  Google Scholar 

  6. A. Dur, The automorphism groups of Reed-Solomon codes, Journal of Combinatorics Theory Ser. A (USA), vol. 44, no.1, Jan. 1987, pp. 69–82.

    Article  Google Scholar 

  7. A. Dur, On the decoding of Reed-Solomon codes, Inter. Conference AAECC7, Toulouse, 26–30 June 1989.

    Google Scholar 

  8. M. Elia, A note on the computation of bit error rate for binary block codes, Journal of Linear Algebra and its Applic., vol. 98, Jan. 1988, pp. 199–210.

    Article  Google Scholar 

  9. R.J. McEliece, L. Swanson, On the Decoder Error Probability for Reed-Solomon Codes, IEEE Trans. on Inform. Theory, vol. IT-32, Sept. 1986, pp. 701–703.

    Article  Google Scholar 

  10. G.C. Rota, Finite Operator Calculus, Academic Press, New York, 1975.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Dipartimento di Elettronica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Torino, Italy

    M. Elia

  2. Centro Ricerche FIAT, Strada Torino 50, 10143, Orbassano, Italy

    G. Taricco

Authors
  1. M. Elia
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  2. G. Taricco
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Editor information

Gérard Cohen Pascale Charpin

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© 1991 Springer-Verlag Berlin Heidelberg

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Elia, M., Taricco, G. (1991). A note on automorphism groups of codes and symbol error probability computation. In: Cohen, G., Charpin, P. (eds) EUROCODE '90. EUROCODE 1990. Lecture Notes in Computer Science, vol 514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54303-1_113

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  • DOI: https://doi.org/10.1007/3-540-54303-1_113

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54303-9

  • Online ISBN: 978-3-540-47546-0

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