In coding theory, the Preparata codes form a class of non-linear double-error-correcting codes. They are named after Franco P. Preparata who firstâ€¦Â (More)

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2010

2010

- Cristina FernÃ¡ndez-CÃ³rdoba, Kevin T. Phelps
- Des. Codes Cryptography
- 2010

The minimum distance graph of an extended Preparata code P (m) has vertices corresponding to codewords and edges corresponding toâ€¦Â (More)

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2009

2009

- Ivan Yu. Mogilnykh
- Probl. Inf. Transm.
- 2009

Let C1 and C2 be codes with code distance d. Codes C1 and C2 are called weakly isometric, if there exists a mapping J : C1 â†’ C2â€¦Â (More)

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2006

2006

- Alexey S. Kuzmin, Viktor T. Markov, Alexander A. Nechaev, A. S. Neljubin
- Discrete Applied Mathematics
- 2006

A classical binary Preparata codeP2(m) is a nonlinear (2m+1, 22(2 âˆ’1âˆ’m), 6)-code, wherem is odd. It has a linear representationâ€¦Â (More)

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1999

1999

- Tor Helleseth, Bo Hove, Kyeongcheol Yang
- IEEE Trans. Information Theory
- 1999

This paper contains results on the generalized Hamming weights for the Goethals and Preparata codes over Z 4 : We give an upperâ€¦Â (More)

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1999

1999

- Tor Helleseth, Chunming Rong, Kyeongcheol Yang
- Discrete Mathematics
- 1999

We consider t-designs constructed from codewords in the Preparata code ~ ove r 2~4. A new approach is given to prove that theâ€¦Â (More)

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1996

1996

The minimum weight codewords in the Preparata code of length n = 4 m are utilized for the construction of an innnite family ofâ€¦Â (More)

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Highly Cited

1995

Highly Cited

1995

- A. Robert Calderbank, N. J. A. Sloane
- Des. Codes Cryptography
- 1995

This paper presents some basic theorems giving the structure of cyclic codes of length n over the ring of integers modulo pa andâ€¦Â (More)

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Highly Cited

1994

Highly Cited

1994

- A. Roger Hammons, P. Vijay Kumar, A. Robert Calderbank, N. J. A. Sloane, Patrick SolÃ©
- IEEE Trans. Information Theory
- 1994

Certain notorious nonlinear binary codes contain more codewords than any known linear code. These include the codes constructedâ€¦Â (More)

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1993

1993

- Andries E. Brouwer, Ludo M. G. M. Tolhuizen
- Des. Codes Cryptography
- 1993

We show for t > 3 the nonexistence of binary [2" 2, 2 t 2t 1, 5] codes. Let a weighted subset of the point set X of the Hammingâ€¦Â (More)

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1993

1993

The Nordstrom-Robinson, Kerdock and (slightly modified) Preparata codes are shown to be linear over 4, the integers mod 4. Theâ€¦Â (More)

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