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Gröbner Basis Cryptosystems
Springer Science and Business Media LLC - Tập 17 - Trang 173-194 - 2006
Peter Ackermann, Martin Kreuzer
In the first sections we extend and generalize Gröbner basis theory to submodules of free right modules over monoid rings. Over free monoids, we adapt the known theory for right ideals and prove versions of Macaulay’s basis theorem, the Buchberger criterion, and the Buchberger algorithm. Over monoids presented by a finitely generated convergent string rewriting system we generalize Madlener’s Gröb...... hiện toàn bộ
Visualizing Properties of Comprehensive SAGBI Bases – Two Examples
Springer Science and Business Media LLC - Tập 12 - Trang 429-435 - 2001
Manfred Göbel
This note presents two examples for the visualization of finiteness and size properties of lexicographical comprehensive SAGBI bases for polynomial invariants of conjugates of the alternating and symmetric group in three variables.
Effective homological computations on finite topological spaces
Springer Science and Business Media LLC - Tập 34 - Trang 33-56 - 2020
Julián Cuevas-Rozo, Laureano Lambán, Ana Romero, Humberto Sarria
The study of topological invariants of finite topological spaces is relevant because they can be used as models of a wide class of topological spaces, including regular CW-complexes. In this work, we present a new module for the Kenzo system that allows the computation of homology groups with generators of finite topological spaces in different situations. Our algorithms combine new constructive v...... hiện toàn bộ
Counting decomposable multivariate polynomials
Springer Science and Business Media LLC - - 2011
Joachim von zur Gathen
New cubic self-dual codes of length 54, 60 and 66
Springer Science and Business Media LLC - Tập 29 - Trang 303-312 - 2017
Pınar Çomak, Jon Lark Kim, Ferruh Özbudak
We study the construction of quasi-cyclic self-dual codes, especially of binary cubic ones. We consider the binary quasi-cyclic codes of length $$3\ell $$ with the algebraic approach of Ling and Solé (IEEE Trans Inf Theory 47(7):2751–2760, 2001. ...... hiện toàn bộ
Fast Algorithms for Zero-Dimensional Polynomial Systems using Duality
Springer Science and Business Media LLC - Tập 14 - Trang 239-272 - 2003
Alin Bostan, Bruno Salvy, Éric Schost
Many questions concerning a zero-dimensional polynomial system can be reduced to linear algebra operations in the quotient algebra A=k[X 1 ,…,X n ]/ℐ, where ℐ is the ideal generated by the input system. Assuming that the multiplicative structure of the algebra A is (partly) known, ...... hiện toàn bộ
Infinite families of t-designs from the binomial $$x^{4}+x^{3}$$ over $$\mathrm {GF}(2^n)$$
Springer Science and Business Media LLC - - 2023
Xin Ling, Can Xiang
EA-inequivalence of bent functions
Springer Science and Business Media LLC - - 2021
Samed Bajrić
Toward involutive bases over effective rings
Springer Science and Business Media LLC - Tập 31 - Trang 359-387 - 2020
Michela Ceria, Teo Mora
In this paper we extend the theory of involutive divisions to the case of monomials with coefficients over effective rings. Moreover, as regards involutive bases, we study the computation of weak involutive bases and sketch a conjecture on strong involutive bases.
Orthogonal matrix and its application in Bloom’s threshold scheme
Springer Science and Business Media LLC - Tập 30 - Trang 147-160 - 2018
Ahmed Mameri, Amar Aissani
Applying the Gram–Schmidt process (also called Gram–Schmidt orthogonalization) to a matrix $$M\in GL(n, {\mathbb {R}})$$ , set of $$n\times n$$ ...... hiện toàn bộ
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