Abstract
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.
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References
T. Beth "Generalizing the Discrete Fourier Transform" Discrete Math., vol. 56, no2–3, pp 95–101, 1985.
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.
P. Camion "Un algorithme de construction des idempotents primitifs d'idéaux d'algèbre sur IFp". Annals of Discrete Math., vol.12, pp55–63, 1982.
P.Camion "Un algorithme de construction des idempotents primitifs d'idéaux sur IFq" C.R.A.S. Paris, t291, serie A (1980).
H.F. De Groote,J.Heintz "Commutative algebras of minimal rank" (preprint).
H. Imai "A theory of two dimensional cyclic codes" Inf. and Control 34,pp1–34, 1977.
H.T.Kung, D.M.Tong "Fast algorithms for partial fraction decomp." S.I.A.M. J. Comp., vol.6,no3, 1977.
J.P.Lafon "Algèbre commutative T2" Chez Hermann, 1977.
D. Lazard "Algorithmes fondamentaux en Algèbre commutative" Astérisque 38–39,pp131–138, 1976.
M.P.Malliavin "Les groupes finis et leurs représentations complexes". Chez Masson, 1981.
A. Poli "Important algebraic calculations for n variable polynomial codes" Discrete Math.,vol.56,no2–3,pp255–265,1985.
A.Poli "Codes dans certaines algèbres modulaires" Thèse d'Etat, Univ.P.Sabatier,Toulouse,F,1978.
A.Poli "Quelques résultats sur les codes polynomiaux à n variables". Revue du CETHEDEC, 4ème Trim.,NS 81–2,pp23–33, 1981.
C. Rigoni "Construction of n variable codes". Disc. Math., vol.56,no2–3,pp 275–281, 1985.
J.H. Van Lint "Coding Theory" Springer Verlag (New York), 1973.
M.Ventou "Contribution à l'étude des codes polynomiaux". Thèse de spécialite,Univ.P.Sabatier,Toulouse,F, 1984.
B.L. Van der Waerden "Modern Algebra" F.Ungar Pub. Co., New York, 1964.
F.J.MacWilliams,N.J.A.Sloane "The theory of Error Corr. codes" North Holland P.Co., 1977.
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.
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© 1986 Springer-Verlag Berlin Heidelberg
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Poli, A. (1986). Construction of primitive idempotents for a variable codes. In: Poli, A. (eds) Applied Algebra, Algorithmics and Error-Correcting Codes. AAECC 1984. Lecture Notes in Computer Science, vol 228. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16767-6_48
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DOI: https://doi.org/10.1007/3-540-16767-6_48
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