Sums of seventh powers of polynomials over a finite field with 8 elements
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Abstract
Let F be a finite field with 8 elements. We study representations ofpolynomials over F as sums and strict sums of seventh powers.
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Car, M.
(2015).
Sums of seventh powers of polynomials over a finite field with 8 elements.
Acta Mathematica Universitatis Comenianae, 84(1), 13-26.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/27/121
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References
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2. M. Car, Sums of (2r + 1)-th powers in the polynomial ring F2m[T], Port. Math. (N.S), Vol 67, Fasc 1, (2010), 13-56.
3. M. Car, Sums of fourth powers of polynomials over a finite field of characteristic 3, Func. and Approx, 38.2, (2008), 195-220.
4. M. Car, Sums of seventh powers in the polynomial ring F2m[T], Port. Math. (N.S), Vol 68, Fasc 3, (2011), 297-316.
5. M. Car, Sums of seventh powers in the ring of polynomials over the finite field with four elements, Acta Math. Univ. Comenianae, Vol 92, 1 (2013), 39-67.
6. M. Car, L. Gallardo, Sums of cubes of polynomials, Acta Arith. 112 (2004), 41-50.
7. G. Effinger and D. Hayes, Additive Number Theory of Polynomials Over a Finite Field. Oxford Mathematical Monographs, Clarendon Press, Oxford (1991).
8. W.J. Ellison, Waring’s problem. Amer. Math. Monthly 78 n 1 (1971), 10-36.
9. L. Gallardo, On the restricted Waring problem over F2n[t]. Acta Arith. 42 (2000), 109-113.
10. L. Gallardo, Every sum of cubes in F4[t] is a strict sum of 6 cubes. Port. Math. 65 (2008), no2, 227-236.
11. L. Gallardo, T.R. Heath-Brown, Every sum of cubes in F2[t] is a strict sum of 6 cubes. Finite Fields and App. 13, (2007), no4, 977-980.
12. L. H Gallardo, L. N. Vaserstein, The strict Waring problem for polynomials rings. J. Number Theory, 128, (2008), 2963-2972.
13. Moreno, F. Castro, Divisiblity properties for covering radius of certain cyclic codes IEEE Trans. Inform. Theory 49 (2003), 3299-3303.
14. R.E.A.C Paley, Theorems on polynomials in a Galois field, Quarterly J. of Math., 4, (1933), 52-63.
15. L.N. Vaserstein, Waring’s problem for algebras over fields. J. Number Theory 26 (1987), 286-298.
16. R.C. Vaughan and T.D. Wooley, Waring’s problem: a survey. In Number Theory for the millenium, III (Urbana, IL, 2000), 301-240.