Abstract
An upper bound is obtained on the number of polynomials over GF(2) that divide a polynomial of degree n over GF(2). This bound is the solution of a maximisation problem under constraints. It is used to show that most binary shortened cyclic codes (irreducible or not) satisfy the Gilbert bound.
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References
S.W. GOLOMB, Shift Register Sequences, Holden-Day, San Francisco 1967.
T. KASAMI, "An upper bound on k/n for affine-invariant codes with fixed d/n", IEEE Trans. Inform. Theory, vol. IT-15, pp. 174–176, January 1969.
F.J. MACWILLIAMS and N.J.A. SLOANE, The Theory of Error Correcting Codes, North-Holland, 1977.
J. JUSTESEN, "A class of constructive asymptotically good algebraic codes", IEEE Trans. Inform. Theory, vol. IT-18, pp. 652–656, September 1972.
E.J. WELDON, "Justesen's construction-The low-rate case", IEEE Trans. Inform. Theory, vol. IT-10, pp. 711–713, September 1973.
R.G. GALLAGER, Information Theory and Reliable Communication, Wiley, New York, 1968.
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© 1986 Springer-Verlag Berlin Heidelberg
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Piret, P. (1986). On the number of divisors of a polynomial over GF(2). 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_61
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DOI: https://doi.org/10.1007/3-540-16767-6_61
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