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《Discrete Mathematics》2022,345(3):112740
In this paper, we construct a number of 4-GDDs where the group sizes are all congruent to 2 (mod 3). We also show that 4-GDDs of type exist for all but a finite number of feasible values of s and t. The largest unknown case has type and has 152 points. A number of 4-GDDs with at most 50 points are also constructed. These include one of type , the last feasible type of the form with at most 50 points for which no 4-GDD was known. 相似文献
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In this paper, we will study Ciani curves in characteristic , in particular their standard forms . It is well-known that any Ciani curve is a non-hyperelliptic curve of genus 3, and its Jacobian variety is isogenous to the product of three elliptic curves. As a main result, we will show that if C is superspecial, then belong to and C is maximal or minimal over . Moreover, in this case we will provide a simple criterion in terms of that tells whether C is maximal (resp. minimal) over . 相似文献
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Let be a finite field of cardinality , which is a finite chain ring, and is an odd positive integer. For any , an explicit representation for the dual code of any -constacyclic code over of length is given. And some dual codes of -constacyclic codes over of length 14 are constructed. For the case of , all distinct self-dual -constacyclic codes over of length are determined. 相似文献
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《Discrete Mathematics》2020,343(3):111721
The -additive codes are subgroups of , and can be seen as a generalization of linear codes over and . A -linear Hadamard code is a binary Hadamard code which is the Gray map image of a -additive code. A partial classification of these codes by using the dimension of the kernel is known. In this paper, we establish that some -linear Hadamard codes of length are equivalent, once is fixed. This allows us to improve the known upper bounds for the number of such nonequivalent codes. Moreover, up to , this new upper bound coincides with a known lower bound (based on the rank and dimension of the kernel). Finally, when we focus on , the full classification of the -linear Hadamard codes of length is established by giving the exact number of such codes. 相似文献
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《Discrete Mathematics》2021,344(12):112616
Substitution boxes (S-boxes) play a central role in block ciphers. In substitution-permutation networks, the S-boxes should be permutation functions over to realize the invertibility of the encryption. More importantly, the S-boxes should have low differential uniformity, high nonlinearity, and high algebraic degree in order to resist differential attacks, linear attacks, and higher order differential attacks, respectively. In this paper, we construct new classes of differentially 4 and 6-uniform permutations by modifying the image of the Dobbertin APN function with over a subfield of . In addition, the algebraic degree and the lower bound of the nonlinearity of the constructed functions are given. 相似文献
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A new a priori estimate for solutions to Navier–Stokes equations is derived. Uniqueness and existence of these solutions in for all is proved in a class of solutions locally differentiable in time with values in , where is the Sobolev space. By the solution a solution to an integral equation is understood. No smallness restrictions on the data are imposed. 相似文献
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In this paper, we construct new families of flag-transitive linear spaces with points and points on each line that admit a one-dimensional affine automorphism group. We achieve this by building a natural connection with permutation polynomials of of a particular form and following the scheme of Pauley and Bamberg in (2008) [14]. 相似文献
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《Discrete Mathematics》2019,342(4):934-942
Fricke, Hedetniemi, Hedetniemi, and Hutson asked whether every tree with domination number has at most minimum dominating sets. Bień gave a counterexample, which allows us to construct forests with domination number and minimum dominating sets. We show that every forest with domination number has at most minimum dominating sets, and that every tree with independence number has at most maximum independent sets. 相似文献
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