Results 31 to 40 of about 143,950 (277)
Stabilizer codes over Frobenius rings [PDF]
2012 IEEE International Symposium on Information Theory Proceedings, 2012 Quantum error-correcting codes over finite fields have been widely studied, but quantum codes over rings have been left largely unexplored. This paper introduces stabilizer codes over finite Frobenius rings and establishes their connection to classical code. Structural properties of stabilizer codes over finite Frobenius rings are established.
Sushma Nadella, Andreas Klappenecker
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Mathematics, 2017 In this study, we consider codes over Euclidean domains modulo their ideals. In the first half of the study, we deal with arbitrary Euclidean domains.
Hajime Matsui
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On the Weight Distribution of Codes over Finite Rings [PDF]
, 2011 Let R > S be finite Frobenius rings for which there exists a trace map T from R onto S as left S modules. Let C:= {x -> T(ax + bf(x)) : a,b in R}. Then C is an S-linear subring-subcode of a left linear code over R.
Byrne, Eimear
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LIFTED CODES OVER FINITE CHAIN RINGS [PDF]
, 2011 In this paper, we study lifted codes over finite chain rings.
Dougherty, Steven T. +2 more
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Left dihedral codes over finite chain rings [PDF]
Discrete Mathematics, 2022 Let $R$ be a finite commutative chain ring, $D_{2n}$ be the dihedral group of size $2n$ and $R[D_{2n}]$ be the dihedral group ring. In this paper, we completely characterize left ideals of $R[D_{2n}]$ (called left $D_{2n}$-codes) when ${\rm gcd}(char(R),n)=1$. In this way, we explore the structure of some skew-cyclic codes of length 2 over $R$ and also
H. Aghili, R. Sobhani
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Some results on free Euclidean self-dual codes over F2+vF2
Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2019 In thispaper, free Euclidean self-dual codes over the ring F2+ v F2 with v2=vof order 4 are considered. A necessary andsufficient condition for the form of the generator matrix of a free Euclideanself-dual code is given.
Refia Aksoy, Fatma Çalışkan
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Simplex Linear Codes Over the Ring F2 + vF2 [PDF]
مجلة جامعة النجاح للأبحاث العلوم الطبيعية, 2008 In this paper, we construct simplex linear codes over the ring of types , where and . We also determine some of their properties. These codes are extension and generalization of simplex codes over the rings .
Mohammed AL-Ashker, Ibtisam Isleem
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Decoding Linear Codes over Chain Rings Given by Parity Check Matrices
Mathematics, 2021 We design a decoding algorithm for linear codes over finite chain rings given by their parity check matrices. It is assumed that decoding algorithms over the residue field are known at each degree of the adic decomposition.
José Gómez-Torrecillas +2 more
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A Note on Linear Codes over Semigroup Rings
Trends in Computational and Applied Mathematics, 2011 . In this paper, we introduced new construction techniques of BCH, alternant, Goppa, Srivastava codes through the semigroup ring B[X; 13Z0] instead of the polynomial ring B[X; Z0], where B is a finite commutative ring with identity, and for these ...
Antonio Aparecido de Andrade +2 more
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The dual of convolutional codes over $\mathbb{Z}_{p^r}$
, 2016 An important class of codes widely used in applications is the class of convolutional codes. Most of the literature of convolutional codes is devoted to con- volutional codes over finite fields.
Napp, Diego +3 more
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