Zobrazeno 1 - 10
of 16
pro vyhledávání: '"Science::Mathematics::Algebra [DRNTU]"'
Autor:
Xiaolu Hou
This thesis is dedicated to the constructions of modular lattices with algebraic methods. The goal is to develop new methods as well as constructing new lattices. There are three methods considered: construction from number fields, construction from
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2d9fecfb490b210d2ff541148bc015df
https://doi.org/10.32657/10356/70653
https://doi.org/10.32657/10356/70653
Publikováno v:
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory, Institute of Electrical and Electronics Engineers, 2014, 60 (3), pp.1496-1507
IEEE Transactions on Information Theory, Institute of Electrical and Electronics Engineers, 2014, 60 (3), pp.1496-1507
Hermitian self-dual abelian codes in a group ring Fq2 [G], where Fq2 is a finite field of order q2 and G is a finite abelian group, are studied. Using the well-known discrete Fourier transform decomposition for a semi-simple group ring, a characteriz
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fcbcf12f9bd78ac523daa106212d247e
https://doi.org/10.1109/tit.2013.2296495
https://doi.org/10.1109/tit.2013.2296495
Autor:
San Ling, Patrick Solé
Publikováno v:
Applicable Algebra in Engineering, Communication and Computing. 14:117-125
Low correlation p-ary sequences with p an odd prime are constructed. They are obtained as Gray images of codewords of a subcode of the generalized Kerdock codes over the ring ℤ p 2. They can be shown to be nonlinear in some precise sense.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::827725ab9e0a57dde29c579f6501618b
https://doi.org/10.1007/s00200-003-0130-8
https://doi.org/10.1007/s00200-003-0130-8
Publikováno v:
ISIT
There is a rich theory of relations between lattices and linear codes over finite fields. However, this theory has been developed mostly with lattice codes for the Gaussian channel in mind. In particular, different versions of what is called Construc
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::10f45e0e1a6465f62561660a5d13dbef
https://doi.org/10.1109/isit.2014.6875249
https://doi.org/10.1109/isit.2014.6875249
Autor:
Tan, Ming Ming
This dissertation is devoted to the study of relative difference sets and circulant weighing matrices using algebraic tools. We are mainly interested in answering the existence problems for these objects: For what values of $v$ and $n$, does a circul
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=od______1392::0f5442a008d079b90374f032fac2cb17
http://hdl.handle.net/10356/62325
http://hdl.handle.net/10356/62325
Autor:
Jin, Lingfei
After the pioneering work of Shor and Steane, we are able to establish links between quantum codes and classical codes with certain self-orthogonality. Therefore, constructing classical self-orthogonal codes with small dimension and large dual distan
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=od______1392::92aed22acf06a9484b6f6af28f870cae
http://hdl.handle.net/10356/52463
http://hdl.handle.net/10356/52463
Publikováno v:
ITW
Nonassociative division algebras have been recently proposed as an alternative way to design fully-diverse spacetime codes. In particular, nonassociative cyclic algebras provide division algebras more easily than their associative counter-part. In th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::94d6519687de49afb5f02aa06069d7ff
http://hdl.handle.net/10220/9144
http://hdl.handle.net/10220/9144
Autor:
San Ling
Publikováno v:
Journal of Algebra. 164(2):563-575
is not available. Accepted version
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::affbd3115348c0d19935a5ef6e9c6ec1
Autor:
Feng, Yongqi
56 p. In this master thesis we study a special kind of central simple algebras called crossed product algebras. We will show how to construct them and study some of their properties, mainly their representation theory and divisibility. In particular,
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=od______1392::6363b99adc1c3162dce5d229785c0ee9
http://hdl.handle.net/10356/57394
http://hdl.handle.net/10356/57394
Publikováno v:
Journal of the European Mathematical Society
Journal of the European Mathematical Society, European Mathematical Society, 2010, 12 (2), pp.529-553
Journal of the European Mathematical Society, 2010, 12 (2), pp.529-553. ⟨10.4171/JEMS/208⟩
Journal of the European Mathematical Society, European Mathematical Society, 2010, 12 (2), pp.529-553
Journal of the European Mathematical Society, 2010, 12 (2), pp.529-553. ⟨10.4171/JEMS/208⟩
Let $\R$ be a real closed field, $ {\mathcal Q} \subset \R[Y_1,...,Y_\ell,X_1,...,X_k], $ with $ \deg_{Y}(Q) \leq 2, \deg_{X}(Q) \leq d, Q \in {\mathcal Q}, #({\mathcal Q})=m,$ and $ {\mathcal P} \subset \R[X_1,...,X_k] $ with $\deg_{X}(P) \leq d, P
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::df7b9858eaebd6ae8dda077277ffba04
https://hal.archives-ouvertes.fr/hal-00521520
https://hal.archives-ouvertes.fr/hal-00521520