共查询到20条相似文献,搜索用时 226 毫秒
2.
We explicitly determine generators of cyclic codes over a non-Galois finite chain ring of length , where p is a prime number and k is a positive integer. We completely classify that there are three types of principal ideals of and four types of non-principal ideals of , which are associated with cyclic codes over of length . We then obtain a mass formula for cyclic codes over of length . 相似文献
4.
5.
Let be the finite field of order q. Let G be one of the three groups , or and let W be the standard n-dimensional representation of G. For non-negative integers m and d we let denote the representation of G given by the direct sum of m vectors and d covectors. We exhibit a minimal set of homogeneous invariant polynomials such that for all cases except when and or . 相似文献
6.
After a brief review of the existing results on permutation binomials of finite fields, we introduce the notion of equivalence among permutation binomials (PBs) and describe how to bring a PB to its canonical form under equivalence. We then focus on PBs of of the form , where n and d are positive integers and . Our contributions include two nonexistence results: (1) If q is even and sufficiently large and , then is not a PB of . (2) If , q is sufficiently large and , then is not a PB of under certain additional conditions. (1) partially confirms a recent conjecture by Tu et al. (2) is an extension of a previous result with . 相似文献
7.
8.
9.
Motivated by the well-known Paley graphs over finite fields and their generalizations, in this paper we explore a natural multiplicative-additive analogue of such graphs arising from vector spaces over finite fields. Namely, if and is an -vector space, is the (undirected) graph with vertex set and edge set . We describe the structure of an arbitrary maximal clique in and provide bounds on the clique number of . In particular, we compute the largest possible value of for arbitrary q and n. Moreover, we obtain the exact value of when is any -vector space of dimension . 相似文献
10.
11.
Let q be a perfect power of a prime number p and be an elliptic curve over given by the equation . For a positive integer n we denote by the number of rational points on E (including infinity) over the extension . Under a mild technical condition, we show that the sequence contains at most 10200 perfect squares. If the mild condition is not satisfied, then is a perfect square for infinitely many n including all the multiples of 12. Our proof uses a quantitative version of the Subspace Theorem. We also find all the perfect squares for all such sequences in the range and . 相似文献
12.
13.
14.
16.
Abraham Rueda Zoca 《Journal of Mathematical Analysis and Applications》2022,505(1):125447
We study the presence of L-orthogonal elements in connection with Daugavet centers and narrow operators. We prove that if and is a Daugavet center with separable range then, for every non-empty -open subset W of , it follows that contains some L-orthogonal to Y. In the context of narrow operators, we show that if X is separable and is a narrow operator, then given and any non-empty -open subset W of then W contains some L-orthogonal u so that . In the particular case that is separable, we extend the previous result to . Finally, we prove that none of the previous results holds in larger density characters (in particular, a counterexample is shown for under the assumption ). 相似文献
17.
18.
19.