Results 11 to 20 of about 173,309,485 (168)
Polar Codes for Automorphism Ensemble Decoding [PDF]
2021 IEEE Information Theory Workshop (ITW), 2021 6 pages, 4 figures, final version of conference paper accepted to IEEE ITW ...
Pillet, C, Bioglio, V, Land, I
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Quantum codes from algebraic curves with automorphisms [PDF]
Condensed Matter Physics, 2008 Let Χ be an algebraic curve of genus g ≥ 2 defined over a field Fq of characteristic p > 0. From Χ, under certain conditions, we can construct an algebraic geometry code C.
T.Shaska
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Automorphisms of Codes in the Grassmann Scheme [PDF]
, 2012 Two mappings in a finite field, the Frobenius mapping and the cyclic shift mapping, are applied on lines in PG($n,p$) or codes in the Grassmannian, to form automorphisms groups in the Grassmanian and in its codes. These automorphisms are examined on two classical coding problems in the Grassmannian.
Etzion, Tuvi, Vardy, Alexander
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On automorphism groups of polar codes [PDF]
CoRROver the past years, Polar codes have arisen as a highly effective class of linear codes, equipped with a decoding algorithm of low computational complexity. This family of codes share a common algebraic formalism with the well-known Reed-Muller codes, which involves monomial evaluations. As useful algebraic codes, more specifically known as decreasing
Jicheng Ma, Guiying Yan
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Geometric Goppa codes on Fermat curves [PDF]
Le Matematiche, 2005 We consider a class of codes defined by Goppa’s algebraic-geometric construction on Fermat curves. Automorphisms and decoding of such codes are investigated.
Antonino Giorgio Spera
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On the Automorphism Group of Polar Codes [PDF]
2021 IEEE International Symposium on Information Theory (ISIT), 2021 The automorphism group of a code is the set of permutations of the codeword symbols that map the whole code onto itself. For polar codes, only a part of the automorphism group was known, namely the lower-triangular affine group (LTA), which is solely based upon the partial order of the code's synthetic channels.
Marvin Geiselhart +4 more
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Automorphisms of real Lie algebras of dimension five or less [PDF]
, 2013 The Lie algebra version of the Krull-Schmidt Theorem is formulated and proved. This leads to a method for constructing the automorphisms of a direct sum of Lie algebras from the automorphisms of its indecomposable components.
Gray, RJ +8 more
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Automorphism Ensemble Decoding of Reed–Muller Codes [PDF]
IEEE Transactions on Communications, 2021 Accepted for Publication in IEEE Transactions on ...
Marvin Geiselhart +4 more
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Contributions to automorphisms of affine spaces [PDF]
, 2013 We study aspects of the group G_n of polynomial automorphisms of the affine space A^n, the so-called affine Cremona group. Shafarevich introduced on G_n the structure of an ind-variety, an infinite-dimensional analogon to a (classical) variety.
Stampfli, Immanuel
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Automorphism groups of Grassmann codes
Finite Fields and Their Applications, 2013 revised ...
Sudhir R. Ghorpade, Krishna V. Kaipa
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