Results 1 to 10 of about 146 (134)
Skew Constacyclic Codes over a Non-Chain Ring [PDF]
Entropy, 2023 In this paper, we investigate the algebraic structure of the non-local ring Rq=Fq[v]/⟨v2+1⟩ and identify the automorphisms of this ring to study the algebraic structure of the skew constacyclic codes and their duals over this ring. Furthermore, we give a
Mehmet Emin Köroğlu, Mustafa Sarı
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Low-Complexity Automorphism Ensemble Decoding of Reed-Muller Codes Using Path Pruning [PDF]
EntropyThe newly developed automorphism ensemble decoder (AED) leverages the rich automorphisms of Reed–Muller (RM) codes to achieve near maximum likelihood (ML) performance at short code lengths.
Kairui Tian, Rongke Liu, Zheng Lu
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On the Dimensions of Hermitian Subfield Subcodes from Higher-Degree Places [PDF]
EntropyThe focus of our research is the examination of Hermitian curves over finite fields, specifically concentrating on places of degree three and their role in constructing Hermitian codes.
Sabira El Khalfaoui, Gábor P. Nagy
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Quasi-Optimal Path Convergence-Aided Automorphism Ensemble Decoding of Reed–Muller Codes [PDF]
EntropyBy exploiting the rich automorphisms of Reed–Muller (RM) codes, the recently developed automorphism ensemble (AE) successive cancellation (SC) decoder achieves a near-maximum-likelihood (ML) performance for short block lengths.
Kairui Tian +3 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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Classification of Automorphisms for the Decoding of Polar Codes
ICC 2022 - IEEE International Conference on Communications, 2022 7 pages, 5 figures, to be submitted in IEEE ICC ...
Charles Pillet +2 more
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Isometry and automorphisms of constant dimension codes
Advances in Mathematics of Communications, 2013 We define linear and semilinear isometry for general subspace codes, used for random network coding. Furthermore, some results on isometry classes and automorphism groups of known constant dimension code constructions are derived.
Anna-Lena Trautmann
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On automorphisms of generalized algebraic-geometry codes
Journal of Pure and Applied Algebra, 2007 In coding theory, one often is interested in codes admitting large automorphism group. Certainly, the knowledge of the automorphism group of a code or even of part of this group gives information about the structure of the code and can allow to developing a decoding algorithm. In [IEEE Trans. Inform. Theory 45, No. 7, 2498--2501 (1999; Zbl 0956.94023)]
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On automorphisms of geometric Goppa codes
Journal of Algebra, 1990 Let \(F/{\mathbb{F}}_ q\) be an algebraic function field of genus g, \(D=P_ 1+...+P_ n\) with pairwise distinct places \(P_ i\) of degree one, and G be another divisor of F such that \(\sup p(G)\cap \sup p(D)=\emptyset\). The geometric Goppa code associated to G and D is by definition \(C(G,D)=\{(x(P_ 1),...,x(P_ n))| x\in L(G)\}\); it is a linear code
Henning Stichtenoth
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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
openaire +2 more sources