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《Discrete Mathematics》2024,347(1):113662
According to the well-known CSS construction, constructing quantum MDS codes are extensively investigated via Hermitian self-orthogonal generalized Reed-Solomon (GRS) codes. In this paper, given two Hermitian self-orthogonal GRS codes and , we propose a sufficient condition to ensure that is still a Hermitian self-orthogonal code. Consequently, we first present a new general construction of infinitely families of quantum MDS codes from known ones. Moreover, applying the trace function and norm function over finite fields, we give another two new constructions of quantum MDS codes with flexible parameters. It turns out that the forms of the lengths of our quantum MDS codes are quite different from previous known results in the literature. Meanwhile, the minimum distances of all the q-ary quantum MDS codes are bigger than . 相似文献
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Julia Semikina 《Journal of Pure and Applied Algebra》2019,223(10):4509-4523
I. Hambleton, L. Taylor and B. Williams conjectured a general formula in the spirit of H. Lenstra for the decomposition of for any finite group G and noetherian ring R. The conjectured decomposition was shown to hold for some large classes of finite groups. D. Webb and D. Yao discovered that the conjecture failed for the symmetric group , but remarked that it still might be reasonable to expect the HTW-decomposition for solvable groups. In this paper we show that the solvable group is also a counterexample to the conjectured HTW-decomposition. Nevertheless, we prove that for any finite group G the rank of does not exceed the rank of the expression in the HTW-decomposition. We also show that the HTW-decomposition predicts correct torsion for for any finite group G. Furthermore, we prove that for any degree other than the conjecture gives a correct prediction for the rank of . 相似文献
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《Discrete Mathematics》2022,345(8):112903
Graphs considered in this paper are finite, undirected and loopless, but we allow multiple edges. The point partition number is the least integer k for which G admits a coloring with k colors such that each color class induces a -degenerate subgraph of G. So is the chromatic number and is the point arboricity. The point partition number with was introduced by Lick and White. A graph G is called -critical if every proper subgraph H of G satisfies . In this paper we prove that if G is a -critical graph whose order satisfies , then G can be obtained from two non-empty disjoint subgraphs and by adding t edges between any pair of vertices with and . Based on this result we establish the minimum number of edges possible in a -critical graph G of order n and with , provided that and t is even. For the corresponding two results were obtained in 1963 by Tibor Gallai. 相似文献
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《Discrete Mathematics》2022,345(10):113004
Let G be a graph. We say that G is perfectly divisible if for each induced subgraph H of G, can be partitioned into A and B such that is perfect and . We use and to denote a path and a cycle on t vertices, respectively. For two disjoint graphs and , we use to denote the graph with vertex set and edge set , and use to denote the graph with vertex set and edge set . In this paper, we prove that (i) -free graphs are perfectly divisible, (ii) if G is -free with , (iii) if G is -free, and (iv) if G is -free. 相似文献
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《Discrete Mathematics》2022,345(11):113059
Let be the finite field of q elements and let be the dihedral group of 2n elements. Left ideals of the group algebra are known as left dihedral codes over of length 2n, and abbreviated as left -codes. Let . In this paper, we give an explicit representation for the Euclidean hull of every left -code over . On this basis, we determine all distinct Euclidean LCD codes and Euclidean self-orthogonal codes which are left -codes over . In particular, we provide an explicit representation and a precise enumeration for these two subclasses of left -codes and self-dual left -codes, respectively. Moreover, we give a direct and simple method for determining the encoder (generator matrix) of any left -code over , and present several numerical examples to illustrative our applications. 相似文献
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Mi Hee Park 《Journal of Pure and Applied Algebra》2019,223(9):3980-3988
There are many Noetherian-like rings. Among them, we are interested in SFT-rings, piecewise Noetherian rings, and rings with Noetherian prime spectrum. Some of them are stable under polynomial extensions but none of them are stable under power series extensions. We give partial answers to some open questions related with stabilities of such rings. In particular, we show that any mixed extensions over a zero-dimensional SFT ring R are also SFT-rings, and that if R is an SFT-domain such that is integrally closed for each prime ideal P of R, then is an SFT-ring. We also give a direct proof that if R is an SFT Prüfer domain, then is an SFT-ring. Finally, we show that the power series extension over a Prüfer domain R is piecewise Noetherian if and only if R is Noetherian. 相似文献
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Md. Ali Zinna 《Journal of Pure and Applied Algebra》2019,223(2):783-793
Let R be a commutative Noetherian ring of dimension two with and let . Let P be a projective A-module of rank 2. In this article, we prove that P is cancellative if is cancellative. 相似文献
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