Fast interpolation and multiplication of unbalanced polynomials
We consider the classical problems of interpolating a polynomial given a black box for
evaluation, and of multiplying two polynomials, in the setting where the bit-lengths of the …
evaluation, and of multiplying two polynomials, in the setting where the bit-lengths of the …
Inverse of the Gomory Corner Relaxation of Integer Programs
F Nosrat, G Lyu, AJ Schaefer - arXiv preprint arXiv:2410.22653, 2024 - arxiv.org
We analyze the inverse of the Gomory corner relaxation (GCR) of a pure integer program
(IP). We prove the inverse GCR is equivalent to the inverse of a shortest path problem …
(IP). We prove the inverse GCR is equivalent to the inverse of a shortest path problem …
Embedding Integer Lattices as Ideals into Polynomial Rings
Y Cheng, Y Feng, Y Pan - … of the 2024 International Symposium on …, 2024 - dl.acm.org
Many lattice-based crypstosystems employ ideal lattices for high efficiency. However, the
additional algebraic structure of ideal lattices usually makes us worry about the security, and …
additional algebraic structure of ideal lattices usually makes us worry about the security, and …
Lower Bounds for the Rank of a Matrix with Zeros and Ones outside the Leading Diagonal
AV Seliverstov, OA Zverkov - Programming and Computer Software, 2024 - Springer
We found a lower bound on the rank of a square matrix where every entry in the leading
diagonal is neither zero nor one and every entry outside the leading diagonal is either zero …
diagonal is neither zero nor one and every entry outside the leading diagonal is either zero …
A cubic algorithm for computing the Hermite normal form of a nonsingular integer matrix
S Birmpilis, G Labahn, A Storjohann - ACM Transactions on Algorithms, 2023 - dl.acm.org
A Las Vegas randomized algorithm is given to compute the Hermite normal form of a
nonsingular integer matrix A of dimension n. The algorithm uses quadratic integer …
nonsingular integer matrix A of dimension n. The algorithm uses quadratic integer …
Calculating the Minimum Distance of a Toric Code via Algebraic Algorithms
F Baldemir, M Şahin - Mathematics in Computer Science, 2023 - Springer
Toric codes are examples of evaluation codes. They are produced by evaluating
homogeous polynomials of a fixed degree at the F q-rational points of a subset Y of a toric …
homogeous polynomials of a fixed degree at the F q-rational points of a subset Y of a toric …
[HTML][HTML] 有关欧拉图Q-道矩阵Smith 标准型的性质研究
魏靖园， 吕思澄 - Pure Mathematics, 2024 - hanspub.org
对n 阶欧拉图G, 考虑其对应的Q-道矩阵, 这里Q 为图G 的无符号拉普拉斯矩阵, e 为n
维全一列向量. 本文给出当WQ 的行列式满足, 其中b 为奇数且不含平方因子时, WQ 的Smith …
维全一列向量. 本文给出当WQ 的行列式满足, 其中b 为奇数且不含平方因子时, WQ 的Smith …
Satisfiability Phase Transtion for Random Quantum 3XOR Games
Recent results showed it was possible to determine if a modest size 3XOR game has a
perfect quantum strategy. We build on these and give an explicit polynomial time algorithm …
perfect quantum strategy. We build on these and give an explicit polynomial time algorithm …
[图书][B] Computer Algebra in Scientific Computing: 25th International Workshop, CASC 2023, Havana, Cuba, August 28–September 1, 2023, Proceedings
One of the main goals of the International Workshops on Computer Algebra in Scientific
Computing, which started in 1998 and since then have been held annually, is the timely in …
Computing, which started in 1998 and since then have been held annually, is the timely in …
ON THE MINIMUM DISTANCE OF A TORIC CODE VIA VANISHING IDEAL
F Baldemir - 2023 - open.metu.edu.tr
Toric codes are examples of evaluation codes produced by evaluating homogeous
polynomials of a fixed degree $\alpha $ at the $\F_q $-rational points of a subset $ Y $ of a …
polynomials of a fixed degree $\alpha $ at the $\F_q $-rational points of a subset $ Y $ of a …