Construction of primitive idempotents for a variable codes

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 228)


We propose an algorithm to construct primitive idempotents in any algebra of the type A=K[X1, ... ,xn]/(t1(x1), ..., tn(xn)). Each polynomial ti has its coefficients in a commutative field K.


Discrete Fourier Transform Finite Field Group Algebra Cyclic Code Minimal Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. (1).
    T. Beth "Generalizing the Discrete Fourier Transform" Discrete Math., vol. 56, no2–3, pp 95–101, 1985.Google Scholar
  2. (2).
    P.Camion "Improving an algorithm for factoring polynomials over a finite field and constructing large irred.pomyn." IEEE Trans. on Inf. Theory,vol. IT29,no3,May 1985.Google Scholar
  3. (3).
    P. Camion "Un algorithme de construction des idempotents primitifs d'idéaux d'algèbre sur IFp". Annals of Discrete Math., vol.12, pp55–63, 1982.Google Scholar
  4. (4).
    P.Camion "Un algorithme de construction des idempotents primitifs d'idéaux sur IFq" C.R.A.S. Paris, t291, serie A (1980).Google Scholar
  5. (5).
    H.F. De Groote,J.Heintz "Commutative algebras of minimal rank" (preprint).Google Scholar
  6. (6).
    H. Imai "A theory of two dimensional cyclic codes" Inf. and Control 34,pp1–34, 1977.Google Scholar
  7. (7).
    H.T.Kung, D.M.Tong "Fast algorithms for partial fraction decomp." S.I.A.M. J. Comp., vol.6,no3, 1977.Google Scholar
  8. (8).
    J.P.Lafon "Algèbre commutative T2" Chez Hermann, 1977.Google Scholar
  9. (9).
    D. Lazard "Algorithmes fondamentaux en Algèbre commutative" Astérisque 38–39,pp131–138, 1976.Google Scholar
  10. (10).
    M.P.Malliavin "Les groupes finis et leurs représentations complexes". Chez Masson, 1981.Google Scholar
  11. (11).
    A. Poli "Important algebraic calculations for n variable polynomial codes" Discrete Math.,vol.56,no2–3,pp255–265,1985.Google Scholar
  12. (12).
    A.Poli "Codes dans certaines algèbres modulaires" Thèse d'Etat, Univ.P.Sabatier,Toulouse,F,1978.Google Scholar
  13. (13).
    A.Poli "Quelques résultats sur les codes polynomiaux à n variables". Revue du CETHEDEC, 4ème Trim.,NS 81–2,pp23–33, 1981.Google Scholar
  14. (14).
    C. Rigoni "Construction of n variable codes". Disc. Math., vol.56,no2–3,pp 275–281, 1985.Google Scholar
  15. (15).
    J.H. Van Lint "Coding Theory" Springer Verlag (New York), 1973.Google Scholar
  16. (16).
    M.Ventou "Contribution à l'étude des codes polynomiaux". Thèse de spécialite,Univ.P.Sabatier,Toulouse,F, 1984.Google Scholar
  17. (17).
    B.L. Van der Waerden "Modern Algebra" F.Ungar Pub. Co., New York, 1964.Google Scholar
  18. (18).
    F.J.MacWilliams,N.J.A.Sloane "The theory of Error Corr. codes" North Holland P.Co., 1977.Google Scholar
  19. (19).
    F.Winkler,B.Buchberger,F.Lichtenberger,H.Rolletschek "An algorithm for constructing canonical bases (Grobner bases) of polynomial ideals". CAMP.Publ.,no81–10,Sept.1981.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • A. Poli
    • 1
  1. 1.AAECC LabUniversité Paul SabatierToulouse cédexFrance

Personalised recommendations