Primitive $t$-nomials $(t=3,5)$ over $\textrm {GF}(2)$ whose degree is a Mersenne exponent $\le 44497$
HTML articles powered by AMS MathViewer
- by Yoshiharu Kurita and Makoto Matsumoto PDF
- Math. Comp. 56 (1991), 817-821 Request permission
Abstract:
All of the primitive trinomials over $GF(2)$ with degree p given by one of the Mersenne exponents 19937, 21701, 23209, and 44497 are presented. Also, one example of a primitive pentanomial over $GF(2)$ is presented for each degree up to 44497 that is a Mersenne exponent. The sieve used is briefly described. A problem is posed which conjectures the number of primitive pentanomials of degree p.References
- Elwyn R. Berlekamp, Algebraic coding theory, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1968. MR 0238597
- Rudolf Lidl and Harald Niederreiter, Introduction to finite fields and their applications, Cambridge University Press, Cambridge, 1986. MR 860948
- Eugene R. Rodemich and Howard Rumsey Jr., Primitive trinomials of high degree, Math. Comp. 22 (1968), 863β865. MR 238813, DOI 10.1090/S0025-5718-1968-0238813-1
- Wayne Stahnke, Primitive binary polynomials, Math. Comp. 27 (1973), 977β980. MR 327722, DOI 10.1090/S0025-5718-1973-0327722-7
- E. J. Watson, Primitive polynomials $(\textrm {mod}\ 2)$, Math. Comp. 16 (1962), 368β369. MR 148256, DOI 10.1090/S0025-5718-1962-0148256-1 N. Zierler and J. Brillhart, On primitive trinomials $\pmod 2$, Inform. and Control 13 (1968), 541-554; II, 14 (1969), 566-569.
- Neal Zierler, Primitive trinomials whose degree is a Mersenne exponent, Information and Control 15 (1969), 67β69. MR 244205, DOI 10.1016/S0019-9958(69)90631-7
Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Math. Comp. 56 (1991), 817-821
- MSC: Primary 11T06; Secondary 11A41
- DOI: https://doi.org/10.1090/S0025-5718-1991-1068813-6
- MathSciNet review: 1068813