共查询到20条相似文献,搜索用时 46 毫秒
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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
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《Comptes Rendus Mathematique》2019,357(8):686-690
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We show that the construction of Gabor frames in with generators in and with respect to time-frequency shifts from a rectangular lattice is equivalent to the construction of certain Gabor frames for over the adeles over the rationals and the group . Furthermore, we detail the connection between the construction of Gabor frames on the adeles and on with the construction of certain Heisenberg modules. 相似文献
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Masoumah Al-Ali 《Journal of Pure and Applied Algebra》2019,223(12):5430-5443
Let be a simple, finite-dimensional complex Lie algebra, and let denote the universal affine vertex algebra associated to at level k. The Cartan involution on lifts to an involution on , and we denote by the orbifold, or fixed-point subalgebra, under this involution. Our main result is an explicit minimal strong finite generating set for for generic values of k. 相似文献
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L. Emily Cowie Hans-Christian Herbig Daniel Herden Christopher Seaton 《Journal of Pure and Applied Algebra》2019,223(1):395-421
Let V be a finite-dimensional representation of the complex circle determined by a weight vector . We study the Hilbert series of the graded algebra of polynomial -invariants in terms of the weight vector a of the -action. In particular, we give explicit formulas for as well as the first four coefficients of the Laurent expansion of at . The naive formulas for these coefficients have removable singularities when weights pairwise coincide. Identifying these cancelations, the Laurent coefficients are expressed using partial Schur polynomials that are independently symmetric in two sets of variables. We similarly give an explicit formula for the a-invariant of in the case that this algebra is Gorenstein. As an application, we give methods to identify weight vectors with Gorenstein and non-Gorenstein invariant algebras. 相似文献
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In this work we give a characterization of Galois Linear Complementary Dual codes and Galois-invariant codes over mixed alphabets of finite chain rings, which leads to the study of the Gray image of -linear codes, where and that provides LCD codes over . 相似文献
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Let p be an odd prime number. We describe the Whitehead group of all extra-special and almost extra-special p-groups. For this we compute, for any finite p-group P, the subgroup of , in terms of a genetic basis of P. We also introduce a deflation map , for a normal subgroup N of P, and show that it is always surjective. Along the way, we give a new proof of the result describing the structure of , when P is an elementary abelian p-group. 相似文献
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Daniel Núñez-Alarcón Daniel Pellegrino Diana Serrano-Rodríguez 《Journal of Mathematical Analysis and Applications》2022,505(2):125520
The Orlicz -mixed inequality states that for all bilinear forms and all positive integers n, where denotes or endowed with the supremum norm. In this paper we extend this inequality to multilinear forms, with endowed with norms for all . 相似文献
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As an extension of Gabor frames, nonstationary Gabor (NSG) frames were recently introduced in adaptive signal analysis. They allow for efficient reconstruction with flexible sampling and varying window functions. In this paper we generalize the notion of NSG frames from to the vector-valued Hilbert space , and investigate the resulting vector-valued NSG frames. We derive a Walnut's representation of the mixed frame operator, and provide some necessary/sufficient conditions for a vector-valued NSG system to be a frame for . Furthermore, we show the existence of painless vector-valued NSG frames, and of vector-valued NSG frames with fast decaying window functions. 相似文献
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Let be its decomposition into a product of powers of two distinct primes, and be the residue class ring modulo h. In this paper, we determine the Smith normal forms of matrices, compute the number of the orbits of matrices under the action of the group and the length of each orbit over . As applications, we determine the clique number, the independence number and the chromatic number of the bilinear forms graph, construct a family of association schemes by using matrices and compute the intersection numbers and the character table over for . 相似文献
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