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LIU Xiu-sheng LIU Hua-lu 《数学季刊》2014,(2):189-194
We study the structure of cyclic codes of an arbitrary length n over the ring F2+uF2+vF2, which is not a finite chain ring. We prove that the Gray image of a cyclic code length n over F2+uF2+vF2 is a 3-quasi-cyclic code length 3n over F2. 相似文献
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ZHANG Xiao-yan 《数学季刊》2014,(2):210-214
In this work, we investigate the cyclic codes over the ring F2+uF2+vF2. We first study the relationship between linear codes over F2+uF2+vF2 and that over F2. Then we give a characterization of the cyclic codes over F2+uF2+vF2. Finally, we obtain the number of the cyclic code over F2+uF2+vF2 of length n. 相似文献
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Koichi Betsumiya T. Aaron Gulliver Masaaki Harada 《Designs, Codes and Cryptography》2003,28(2):171-186
In this paper, it is shown that extremal (Hermitian) self-dual codes over
2 ×
2 exist only for lengths 1, 2, 3, 4, 5, 8 and 10. All extremal self-dual codes over
2 ×
2 are found. In particular, it is shown that there is a unique extremal self-dual code up to equivalence for lengths 8 and 10. Optimal self-dual codes are also investigated. A classification is given for binary [12, 7, 4] codes with dual distance 4, binary [13, 7, 4] codes with dual distance 4 and binary [13, 8, 4] codes with dual distance 4. 相似文献
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A. S. Morozov 《Siberian Mathematical Journal》2014,55(1):125-131
We prove that the semigroup of all functions from the set of natural numbers to natural numbers by composition has no one-valued Σ-presentations with parameters over the hereditarily finite superstructure over the real numbers. 相似文献
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Let T be a bounded linear operator on a complex Hilbert space H. In this paper we introduce a new class denoted by l-*-A, of operators satisfying T*|T2|T≥ T*|T*|2T, and we prove the basic properties of these operators. Using these results, we also prove that if T or T* ∈l-*-A, then w(f(T)) = f(w(T)), σea(f(T)) = f(σea(T)) for every f C H(σ(T)), where g(σ(T)) denotes the set of all analytic functions on an open neighborhood of σ(T). 相似文献
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《Annals of Pure and Applied Logic》2019,170(12):102719
We provide algebraic conditions ensuring the decidability of the theory of modules over effectively given Prüfer (in particular Bézout) domains whose localizations at maximal ideals have dense value groups. For Bézout domains, these conditions are also necessary. 相似文献
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Paul Feit 《Israel Journal of Mathematics》1990,69(3):289-320
Letf(X; T 1, ...,T n) be an irreducible polynomial overQ. LetB be the set ofb teZ n such thatf(X;b) is of lesser degree or reducible overQ. Let ?={F j}{F j } j?1 ∞ be a Følner sequence inZ n — that is, a sequence of finite nonempty subsetsF j ?Z n such that for eachvteZ n , $\mathop {lim}\limits_{j \to \infty } \frac{{\left| {F_j \cap (F_j + \upsilon )} \right|}}{{\left| {F_j } \right|}} = 1$ Suppose ? satisfies the extra condition that forW a properQ-subvariety ofP n ?A n and ?>0, there is a neighborhoodU ofW(R) in the real topology such that $\mathop {lim sup}\limits_{j \to \infty } \frac{{\left| {F_j \cap U} \right|}}{{\left| {F_j } \right|}}< \varepsilon $ whereZ n is identified withA n (Z). We prove $\mathop {lim}\limits_{j \to \infty } \frac{{\left| {F_j \cap B} \right|}}{{\left| {F_j } \right|}} = 0$ . 相似文献
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Permutations with low differential uniformity are widely used in cipher design. Recently, Bracken, Tan and Tan (2012) [5] presented a method to construct differentially 4-uniform permutations by changing certain conditions of known APN functions. They guessed that only two classes of existing quadratic APN functions have this property. They succeeded in proving one class and left the other one as an open problem. In this paper, with the help of a computer, those polynomials are proved to be differentially 4-uniform but may not be permutation polynomials, which give a negative answer to this problem. 相似文献
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The present note determines the structure of the K2-group and of itssubgroup over a finite commutative ring R by considering relations between R andfinite commutative local ring Ri (1 ≤ i ≤ m), where R ≌ m i=1 Ri and K2(R) ≌ m i=1 K2(Ri). We show that if charKi = p (Ki denotes the residual field of Ri), then K2(Ri) and its subgroups must be p-groups. 相似文献
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The present note determines the structure of the K2-group and of its subgroup over a finite commutative ring R by considering relations between R and
finite commutative local ring Ri (1 < i < m), where R Ri and K2(R) =
K2(Ri). We show that if charKi= p (Ki denotes the residual field of Ri), then
K2(Ri) and its subgroups must be p-groups. 相似文献
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LiPing Huang 《中国科学A辑(英文版)》2009,52(11):2404-2418
Let D be a division ring with an involution-,H2(D) be the set of 2 × 2 Hermitian matrices over D. Let ad(A,B) = rank(A-B) be the arithmetic distance between A,B ∈ H2(D) . In this paper,the fundamental theorem of the geometry of 2 × 2 Hermitian matrices over D(char(D) = 2) is proved:if :H2(D) → H2(D) is the adjacency preserving bijective map,then is of the form (X) = tP XσP +(0) ,where P ∈ GL2(D) ,σ is a quasi-automorphism of D. The quasi-automorphism of D is studied,and further results are obtained. 相似文献
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We first consider the group inverses of the block matrices ( A 0 B C ) over a weakly finite ring. Then we study the sufficient and necessary conditions for the existence and the representations of the group inverses of the block matrices ( A C B D ) over a ring with unity 1 under the following conditions respectively: (i) B = C, D = 0, B# and (BπA) # both exist; (ii) B is invertible and m = n; (iii) A# and (D - CA#B)# both exist, C = CAA# , where A and D are m × m and n × n matrices, respectively. 相似文献
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Variational perturbation theory is used to study the anharmonic
2k
oscillator in the strong coupling limit. Nonperturbative expressions are obtained for the vacuum energy, the Green's function, and the effective potential.Joint Institute for Nuclear Research, Dubna. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 90, No. 1, pp. 37–54, January, 1992. 相似文献
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本文研究了环F2m+uF2m+u2 Fm+u3F2m上线性码.利用环是Frobenius环,证明了环上线性码C及其自对偶码的Gray像为F2m上的线性码和自对偶码.同时,给出了上循环码C的Gray像ψ(C)为F2m上的拟循环码. 相似文献
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Christine Bachoc T. Aaron Gulliver Masaaki Harada 《Journal of Algebraic Combinatorics》2000,12(3):223-240
A code is called isodual if it is equivalent to its dual code, and a lattice is called isodual if it is isometric to its dual lattice. In this note, we investigate isodual codes over 2k
. These codes give rise to isodual lattices; in particular, we construct a 22-dimensional isodual lattice with minimum norm 3 and kissing number 2464. 相似文献