Automorphism groups of cyclic codes Rolf Bienert · Benjamin Klopsch
... Interestingly, some of the codes C0 (a, b) were recently studied by Key and Seneviratne in the context of regular lattice graphs and permutation decoding. In fact, we provide a new, unified treatment of a related family C1 (a, b) of binary linear codes whose study was initiated in [5]. Our approach ...
... Interestingly, some of the codes C0 (a, b) were recently studied by Key and Seneviratne in the context of regular lattice graphs and permutation decoding. In fact, we provide a new, unified treatment of a related family C1 (a, b) of binary linear codes whose study was initiated in [5]. Our approach ...
Elements of Modern Algebra
... As the earlier editions were, this book is intended as a text for an introductory course in algebraic structures (groups, rings, fields, and so forth). Such a course is often used to bridge the gap from manipulative to theoretical mathematics and to help prepare secondary mathematics teachers for th ...
... As the earlier editions were, this book is intended as a text for an introductory course in algebraic structures (groups, rings, fields, and so forth). Such a course is often used to bridge the gap from manipulative to theoretical mathematics and to help prepare secondary mathematics teachers for th ...
DIRECTED HOMOTOPY THEORY, II. HOMOTOPY CONSTRUCTS
... including their ‘exactness property’ (Theorem 2.5), by comparison with sequences of iterated mapping (co)cones, alternatively lower or upper. Note that, even if paths in a d-space X cannot be reversed, generally, they can nevertheless be reflected in the opposite object RX = X op ; thus, lower and up ...
... including their ‘exactness property’ (Theorem 2.5), by comparison with sequences of iterated mapping (co)cones, alternatively lower or upper. Note that, even if paths in a d-space X cannot be reversed, generally, they can nevertheless be reflected in the opposite object RX = X op ; thus, lower and up ...
Fascicule 1
... and codomain, Banaschewski and Herrlich [5] characterized full subcategories of “suitable” categories which can be specified by such injectivity: they are precisely the subcategories closed under products, subobjects, and filtered colimits. Recently the same result was proved for all locally finitel ...
... and codomain, Banaschewski and Herrlich [5] characterized full subcategories of “suitable” categories which can be specified by such injectivity: they are precisely the subcategories closed under products, subobjects, and filtered colimits. Recently the same result was proved for all locally finitel ...
Some topics in the theory of finite groups
... only if the numbers m1 , . . . , mr and k are the same for the two groups. Alternatively, all finite abelian groups are direct products of cyclic groups of prime power order. This follows from the fact that if m and n are relatively prime then Cm ×Cn ∼ ...
... only if the numbers m1 , . . . , mr and k are the same for the two groups. Alternatively, all finite abelian groups are direct products of cyclic groups of prime power order. This follows from the fact that if m and n are relatively prime then Cm ×Cn ∼ ...
Weyl Groups Associated with Affine Reflection Systems of Type
... In [AYY], the authors introduce an equivalent definition for an affine reflection system (see Definition 1.1) which we will use it here. In finite and affine cases, the corresponding Weyl groups are fairly known. In particular, they are known to be Coxeter groups and that through their actions imple ...
... In [AYY], the authors introduce an equivalent definition for an affine reflection system (see Definition 1.1) which we will use it here. In finite and affine cases, the corresponding Weyl groups are fairly known. In particular, they are known to be Coxeter groups and that through their actions imple ...
Galois Theory - Joseph Rotman
... algebra" (that is, a first course which mentions rings, groups, and homomorphisms). In spite of this, a discussion of commutative rings, starting from the definition, begins the text. This account is written in the spirit of a review of things past, and so, even though it is complete, it may be too ...
... algebra" (that is, a first course which mentions rings, groups, and homomorphisms). In spite of this, a discussion of commutative rings, starting from the definition, begins the text. This account is written in the spirit of a review of things past, and so, even though it is complete, it may be too ...
The Relationship Between Two Commutators
... Conditions (1) and (2) imply that for any A ∈ V ∗ we have p(x, y, z) = x − y + z with respect to some abelian group structure on A. We call a structure of the form hA; pi where p satisfies (1) and (2) an affine abelian group. Condition (3) says that every basic τ –operation is multilinear with resp ...
... Conditions (1) and (2) imply that for any A ∈ V ∗ we have p(x, y, z) = x − y + z with respect to some abelian group structure on A. We call a structure of the form hA; pi where p satisfies (1) and (2) an affine abelian group. Condition (3) says that every basic τ –operation is multilinear with resp ...
On fusion categories - Annals of Mathematics
... is an integer, then it coincides with the global dimension. This result may be regarded as a categorical version of the well-known theorem of Larson and Radford, saying that the antipode of a semisimple Hopf algebra is involutive. Further, we show that the Frobenius-Perron dimension of a fusion cate ...
... is an integer, then it coincides with the global dimension. This result may be regarded as a categorical version of the well-known theorem of Larson and Radford, saying that the antipode of a semisimple Hopf algebra is involutive. Further, we show that the Frobenius-Perron dimension of a fusion cate ...
CLASSIFICATION OF PRINCIPAL BUNDLES AND LIE GROUPOIDS
... that couplings of G with N are in bijective correspondence with abstract kernels G + Out(N). Some examples of crossed modules which are not couplings are given at the end of the section. For further examples, history and references see [3, $31. Consider groups G and N and let y : G + Out(N) be an ab ...
... that couplings of G with N are in bijective correspondence with abstract kernels G + Out(N). Some examples of crossed modules which are not couplings are given at the end of the section. For further examples, history and references see [3, $31. Consider groups G and N and let y : G + Out(N) be an ab ...
FILTERED MODULES WITH COEFFICIENTS 1. Introduction Let E
... Savitt [Sav05] has treated cases where ρ becomes crystalline over a tamely ramified extension of Qp . In this paper we will extend some of the results in these papers. In particular we will treat cases where ρ becomes crystalline over wildly ramified extensions of Qp . A novel feature of our work is ...
... Savitt [Sav05] has treated cases where ρ becomes crystalline over a tamely ramified extension of Qp . In this paper we will extend some of the results in these papers. In particular we will treat cases where ρ becomes crystalline over wildly ramified extensions of Qp . A novel feature of our work is ...
