The Etzion-Silberstein conjecture holds for every Ferrers diagram if and only if it holds for the irreducible ones, which are precisely the integer points of integral polytopes in R^{2d-3} for each d.
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Symmetric tensor ranks of finite-field multiplication are recast as linear-algebra spanning problems over finite fields, with new criteria, recovered values for small degrees, and a matching invariant for one-dimensional Gabidulin codes.
b_2(5,2,2;s) is completely determined as a function of s via integer linear programming on the projective geometry PG(4,2), with additional bounds and constructions for other n_q and b_q parameters.
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Irreducible Ferrers diagrams in the Etzion-Silberstein conjecture
The Etzion-Silberstein conjecture holds for every Ferrers diagram if and only if it holds for the irreducible ones, which are precisely the integer points of integral polytopes in R^{2d-3} for each d.
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Symmetric Tensor Decompositions over Finite Fields
Symmetric tensor ranks of finite-field multiplication are recast as linear-algebra spanning problems over finite fields, with new criteria, recovered values for small degrees, and a matching invariant for one-dimensional Gabidulin codes.
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Generalized Hamming weights of additive codes and geometric counterparts
b_2(5,2,2;s) is completely determined as a function of s via integer linear programming on the projective geometry PG(4,2), with additional bounds and constructions for other n_q and b_q parameters.