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A table of irreducible polynomials and their exponents

Published online by Cambridge University Press:  24 October 2008

J. A. Chang  and
H. J. Godwin
J. A. Chang
Affiliation:
University College of Swansea
H. J. Godwin
Affiliation:
University College of Swansea
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Extract

With a view to applications to electrical engineering we have recently calculated the primitive polynomials of degree 2 and 3 modulo various primes. In the course of the work we also obtained all the irreducible polynomials of these kinds and, as an extension of the tables of Church(1), Marsh(2), Peterson(3) and Lloyd(4) we now publish them. Since our primary interest was the exponent to which each polynomial belonged (see Albert(5), p. 130) we group them according to exponent.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 65 , Issue 2 , March 1969 , pp. 513 - 522
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

REFERENCES

(1)Church, R.Tables of irreducible polynomials for the first four prime moduli. Ann. of Math. 36 (1935), 198–209.CrossRefGoogle Scholar
(2)Marsh, R. W.Table of Irreducible Polynomials over GF(2) Through Degree 19 (National Security Administration, Washington, D.C., 1957).Google Scholar
(3)Peterson, W. W.Error-correcting codes (M.I.T., 1961 and John Wiley, New York and London 1961).Google Scholar
(4)Lloyd, D. B.The use of finite polynomial rings in the factorization of the general polynomial. J. Res. Nat. Bur. Standards Sect. B 69 (1965), 189–212.CrossRefGoogle Scholar
(5)Albert, A. A.Fundamental concepts of higher algebra (Univ. of Chicago Press, 1965).Google Scholar