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Every Polymer Over a Finite Field of Even Cardinal q>4 is a Strict Sum of Four Cubes and One Expression A^{2} + A (pp. 213224) 
$45.00 

Authors: Luis H. Gallardo

Abstract: Let q be a power of 2. Let M(q) = {P ∈ F_{q}[t]: P is a strict sum of cubes}. We know that M(q) = F_{2}[t] if and only if q > 4. Every polynomial P ∈ M(q) is a strict sum
P = A^{2}+A+B^{3}+C^{3}+D^{3}+E^{3}.
The polynomials A,B,C,D,E are effectively obtained from the coefficients of P. The proof uses the new result that every polynomial Q ∈ F_{q}[t], satisfying the necessary condition that the constant term Q(0) has zero trace, has a strict and effective representation as:
Q = F^{2}+F +tG^{2}.
This improves a result of Gallardo, Rahavandrainy and Vaserstein that requires three polynomials F,G,H for the strict representation Q = F^{2}+F+GH. Observe that the latter representation may be considered as an analogue in characteristic 2 of the strict representation of a polynomial Q by three squares in odd characteristic.












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