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- Mark F. Flanagan, Vitaly Skachek, Eimear Byrne, Marcus Greferath
- IEEE Transactions on Information Theory
- 2009

A framework for linear-programming (LP) decoding of nonbinary linear codes over rings is developed. This framework facilitates LP-based reception for coded modulation systems which use direct modulation mapping of coded symbols. It is proved that the resulting LP decoder has the ldquomaximum-likelihood (ML) certificaterdquo property. It is also shown that… (More)

- Marcus Greferath, Stefan E. Schmidt
- J. Comb. Theory, Ser. A
- 2000

The theory of linear codes over finite fields has been extended by A. Nechaev to codes over quasi-Frobenius modules over commutative rings, and by J. Wood to codes over (not necessarily commutative) finite Frobenius rings. In the present paper we subsume these results by studying linear codes over quasi-Frobenius and Frobenius modules over any finite ring.… (More)

- Eimear Byrne, Marcus Greferath, Michael E. O'Sullivan
- Des. Codes Cryptography
- 2007

- Eimear Byrne, Marcus Greferath, Thomas Honold
- Des. Codes Cryptography
- 2008

It is known that a linear two-weight code C over a finite field F q corresponds both to a multiset in a projective space over F q that meets every hyperplane in either a or b points for some integers a < b , and to a strongly regular graph whose vertices may be identified with the codewords of C. Here we extend this classical result to the case of a… (More)

- Marten van Dijk, Sebastian Egner, Marcus Greferath, Alfred Wassermann
- IEEE Transactions on Information Theory
- 2005

This correspondence revisits the idea of constructing a binary [mn,mk] code from an [n,k] code over F/sub 2//sup m/ by concatenating the code with a suitable basis representation of F/sub 2//sup m/ over F/sub 2/. We construct two nonequivalent examples of doubly even self-dual binary codes of length 160 which turn out to be of minimum distance 24. This… (More)

- Marcus Greferath, Stefan E. Schmidt
- IEEE Trans. Information Theory
- 1999

- Marcus Greferath, Michael E. O'Sullivan
- Discrete Mathematics
- 2004

- Marcus Greferath, Ute Vellbinger
- IEEE Trans. Information Theory
- 1998

- Iwan M. Duursma, Marcus Greferath, Simon Litsyn, Stefan E. Schmidt
- IEEE Trans. Information Theory
- 2001