Results 11 to 20 of about 145 (141)
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.
Geiselhart, Marvin +4 more
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Automorphisms of hyperelliptic GAG-codes
Electronic Notes in Discrete Mathematics, 2006 Generalized algebraic-geometry codes are linear codes which generalize the well-known geometric Goppa codes, since their construction makes use of places which are not necessarily of degree one. In this paper authors determine the \(n\)-automorphism group of generalized algebraic-geometry codes associated with rational, elliptic and hyperelliptic ...
PICONE, Alberto, SPERA, Antonino Giorgio
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Generic BCH codes. Polynomial-norm error decoding
Журнал Белорусского государственного университета: Математика, информатика, 2020 The classic Bose – Chaudhuri – Hocquenghem (BCH) codes is famous and well-studied part in the theory of error-correcting codes. Generalization of BCH codes allows us to expand the range of activities in the practical correction of errors.
Alexander V. Kushnerov +1 more
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Automorphism groups of some AG codes [PDF]
IEEE Transactions on Information Theory, 2006 added a reference, fixed error in remark ...
Joyner, David, Ksir, Amy
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Properties of triple error orbits G and their invariants in Bose – Chaudhuri – Hocquenghem codes C7
Весці Нацыянальнай акадэміі навук Беларусі: Серыя фізіка-тэхнічных навук, 2019 This work is the further development of the theory of norms of syndromes: the theory of polynomial invariants of G-orbits of errors expands with the group G of automorphisms of binary cyclic BCH codes obtained by joining the degrees of cyclotomic ...
V. A. Lipnitski, A. U. Serada
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Automorphism groups of Gabidulin-like codes [PDF]
Archiv der Mathematik, 2016 Let K be a cyclic Galois extension of degree f over k and T a generator of the Galois group. For any v=(v_1,... , v_m)\in K^m such that v is linearly independent over k, and any 0< d < m the Gabidulin-like code C(v, T , d) is a maximum rank distance code in the space of f times m matrices over k of dimension fd. This construction unifies the ones
Dirk Liebhold, Gabriele Nebe
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Automorphism groups of Grassmann codes
Finite Fields and Their Applications, 2013 revised ...
GHORPADE, SR, KAIPA, KV
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Quantum computation from dynamic automorphism codes [PDF]
QuantumWe propose a new model of quantum computation comprised of low-weight measurement sequences that simultaneously encode logical information, enable error correction, and apply logical gates.
Margarita Davydova +3 more
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Automorphisms of doubly even self-dual binary codes [PDF]
Bulletin of the London Mathematical Society, 2009 Added a new proof for the main ...
Guenther, Annika, Nebe, Gabriele
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Automorphism Groups of BWD-codes
Journal of Combinatorial Theory, Series A, 1997 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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