Keyword

dual codes

Description: In coding theory, dual codes are sets of vectors orthogonal to every codeword of a given code under a specified inner product.

Primary topic: Coding theory and cryptography (90%)

Wikidata ID: wiki/Q5310189

OpenAlex ID: keywords/dual-codes

The Theory of Error-Correcting Codes

1977 · North-Holland mathematical library · 10,812

Convolutional codes I: Algebraic structure

1970 · G. Forney · IEEE Transactions on Information Theory · 766

Extrinsic information transfer functions: model and erasure channel properties

2004 · A. Ashikhmin, G. Kramer, et al. · IEEE Transactions on Information Theory · 756

Codes on graphs: normal realizations

2001 · G.D. Forney · IEEE Transactions on Information Theory · 645

A Theorem on the Distribution of Weights in a Systematic Code†

1963 · Jessie Macwilliams · Bell System Technical Journal · 415

Cyclic and Negacyclic Codes Over Finite Chain Rings

2004 · H.Q. Dinh, S.R. Lopez-Permouth · IEEE Transactions on Information Theory · 393

On Quantum and Classical BCH Codes

2007 · Salah A. Aly, Andreas Klappenecker, et al. · IEEE Transactions on Information Theory · 382

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Four fundamental parameters of a code and their combinatorial significance

1973 · Philippe Delsarte · Information and Control · 304

The weights of the orthogonals of the extended quadratic binary Goppa codes

1990 · G. Lachaud, J. Wolfmann · IEEE Transactions on Information Theory · 281

Finding the permutation between equivalent linear codes: the support splitting algorithm

2000 · N. Sendrier · IEEE Transactions on Information Theory · 269

Enlargement of Calderbank-Shor-Steane quantum codes

1999 · A.M. Steane · IEEE Transactions on Information Theory · 264

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Minimal Codewords and Secret Sharing

1999 · James L. Massey · 244

Cyclic codes and quadratic residue codes over Z/sub 4/

1996 · V.S. Pless, Zhongqiang Qian · IEEE Transactions on Information Theory · 215

Coding with skew polynomial rings

2008 · Delphine Boucher, Felix Ulmer · Journal of Symbolic Computation · 197

Low-density MDS codes and factors of complete graphs

1999 · Lihao Xu, V. Bohossian, et al. · IEEE Transactions on Information Theory · 183

A class of low-rate nonlinear binary codes

1972 · A.M. Kerdock · Information and Control · 181

$${{{\mathbb Z}_2}{{\mathbb Z}_4}}$$ -linear codes: generator matrices and duality

2009 · J. Borges, C. Fernández-Córdoba, et al. · Designs Codes and Cryptography · 180

Projective Reed-Muller codes

1991 · A.B. Sorensen · IEEE Transactions on Information Theory · 178

A class of three-weight cyclic codes

2013 · Zhengchun Zhou, Cunsheng Ding · Finite Fields and Their Applications · 165

Self-dual codes over GF(4)

1978 · F.J MacWilliams, A.M Odlyzko, et al. · Journal of Combinatorial Theory Series A · 155

Cyclic Codes over the Integers Modulopm

1997 · Pramod Kanwar, Sergio R. López-Permouth · Finite Fields and Their Applications · 154

Structural analysis of convolutional codes via dual codes

1973 · G. Forney · IEEE Transactions on Information Theory · 150

Binary Linear Codes With Three Weights

2014 · Kelan Ding, Cunsheng Ding · IEEE Communications Letters · 148

Algebraic structure of quasicyclic codes

2001 · Kristine Lally, Patrick Fitzpatrick · Discrete Applied Mathematics · 147

Quantum Analog of the MacWilliams Identities for Classical Coding Theory

1997 · Peter Shor, Raymond Laflamme · Physical Review Letters · 139

Works count: 1,974

Citation count: 33,950