Irreducible polynomials over finite fields with linearly independent roots

Štefan Schwarz

Mathematica Slovaca (1988)

  • Volume: 38, Issue: 2, page 147-158
  • ISSN: 0139-9918

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Schwarz, Štefan. "Irreducible polynomials over finite fields with linearly independent roots." Mathematica Slovaca 38.2 (1988): 147-158. <http://eudml.org/doc/34273>.

@article{Schwarz1988,
author = {Schwarz, Štefan},
journal = {Mathematica Slovaca},
keywords = {roots of a given irreducible polynomial over a finite field; normal basis},
language = {eng},
number = {2},
pages = {147-158},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Irreducible polynomials over finite fields with linearly independent roots},
url = {http://eudml.org/doc/34273},
volume = {38},
year = {1988},
}

TY - JOUR
AU - Schwarz, Štefan
TI - Irreducible polynomials over finite fields with linearly independent roots
JO - Mathematica Slovaca
PY - 1988
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 38
IS - 2
SP - 147
EP - 158
LA - eng
KW - roots of a given irreducible polynomial over a finite field; normal basis
UR - http://eudml.org/doc/34273
ER -

References

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  1. CONWAY J. H., A tabulation of some information concerning finite fields, Computers in Mathematical Research, North-Holland, Amsterdam, 1968, 37-50. (1968) Zbl0186.07602MR0237467
  2. LIDL R., NIEDERREITER H., Finite Fields, Addison-Wesley Publ. Comp., Reading, Mass., 1983. (1983) Zbl0554.12010MR0746963
  3. ORE O., Contributions to the theory of finite fields, Trans. Amer. Mat. Soc. 36, 1934, 243-274. (1934) Zbl0009.10003MR1501740
  4. PEI D. Y., WANG C. C., OMURA J. K., Normal basis offinite field GF(2m), IEEE Trans. on Inform. Theory, IT-32, 1986, 285-287. (1986) MR0838417
  5. PERLIS S., Normal bases of cyclic fields of prime-power degree, Duke Math. J. 9, 1942, 507-517. (1942) MR0007005
  6. PETERSON W. W., WELDON E. J., Error-Correcting Codes, M.I.T. Press, Cambridge, Mass., 1972. (1972) Zbl0251.94007MR0347444
  7. SCHWARZ Š., On the reducibility of binomial congruences and the bound of the least integer belonging to a given exponent (mod p), Časop. pěst. mat. fys. 74, 1949, 1-16. (1949) MR0032669
  8. SCHWARZ Š., On the reducibility of polynomials over a finite field, Quart. J. of Math. Oxford (2), 7, 1956, 110-124. (1956) Zbl0071.01703MR0096679
  9. SCHWARZ Š., Construction of normal bases in cyclic extensions of a field, (To appear in the Czech. Math. J.) Zbl0671.12006MR0946299

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