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211.
Hennie De Schepper Alí Guzmán Adán Frank Sommen 《Journal of Mathematical Analysis and Applications》2018,457(1):23-50
In [4] we studied the group invariance of the inner product of supervectors as introduced in the framework of Clifford analysis in superspace. The fundamental group leaving invariant such an inner product turns out to be an extension of and gives rise to the definition of the spin group in superspace through the exponential of the so-called extended superbivectors, where the spin group can be seen as a double covering of by means of the representation . In the present paper, we study the invariance of the Dirac operator in superspace under the classical H and L actions of the spin group on superfunctions. In addition, we consider the Hermitian Clifford setting in superspace, where we study the group invariance of the Hermitian inner product of supervectors introduced in [3]. The group of complex supermatrices leaving this inner product invariant constitutes an extension of and is isomorphic to the subset of of elements that commute with the complex structure J. The realization of within the spin group is studied together with the invariance under its actions of the super Hermitian Dirac system. It is interesting to note that the spin element leading to the complex structure can be expressed in terms of the n-dimensional Fourier transform. 相似文献
212.
We investigate the relationship between two constructions of maximal comma-free codes described, respectively, by Eastman and by Scholtz and the notions of Hall sets and Lazard sets introduced in connection with factorizations of free monoids and bases of free Lie algebras. 相似文献
213.
Generalizing the quasi-cyclic codes of index introduced by Fan et al., we study a more general class of quasi-cyclic codes of fractional index generated by pairs of polynomials. The parity check polynomial and encoder of these codes are obtained. The asymptotic behaviours of the rates and relative distances of this class of codes are studied by using a probabilistic method. We prove that, for any positive real number such that the asymptotic GV-bound at is greater than , the relative distance of the code is convergent to , while the rate is convergent to . As a result, quasi-cyclic codes of fractional index are asymptotically good. 相似文献
214.
C.A. Castillo-Guillén C. Rentería-Márquez H. Tapia-Recillas 《Discrete Mathematics》2018,341(4):919-933
Duals of constacyclic codes over a finite local Frobenius non-chain ring of length 4, the length of which is relatively prime to the characteristic of the residue field of the ring are determined. Generators for the dual code are obtained from those of the original constacyclic code. In some cases self-dual codes are determined. 相似文献
215.
In this paper we study a key example of a Hermitian symmetric space and a natural associated double flag variety, namely for the real symplectic group G and the symmetric subgroup L, the Levi part of the Siegel parabolic . We give a detailed treatment of the case of the maximal parabolic subgroups Q of L corresponding to Grassmannians and the product variety of and ; in particular we classify the L-orbits here, and find natural explicit integral transforms between degenerate principal series of L and G. 相似文献
216.
Maria Montanucci 《代数通讯》2018,46(11):4739-4776
217.
Polycyclic codes are a powerful generalization of cyclic and constacyclic codes. Their algebraic structure is studied here by the theory of invariant subspaces from linear algebra. As an application, a bound on the minimum distance of these codes is derived which outperforms, in some cases, the natural analogue of the BCH bound. 相似文献
218.
219.
In this paper1, we prove existence of optimal complementary dual codes (LCD codes) over large finite fields. We also give methods to generate orthogonal matrices over finite fields and then apply them to construct LCD codes. Construction methods include random sampling in the orthogonal group, code extension, matrix product codes and projection over a self-dual basis. 相似文献
220.
In this paper, by employing some results on Kummer extensions, we give an arithmetic characterization of pure Weierstrass gaps at many totally ramified places on a quotient of the Hermitian curve, including the well-studied Hermitian curve as a special case. The cardinality of these pure gaps is explicitly investigated. In particular, the numbers of gaps and pure gaps at a pair of distinct places are determined precisely, which can be regarded as an extension of the previous work by Matthews (2001) considered Hermitian curves. Additionally, some concrete examples are provided to illustrate our results. 相似文献