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- Claudio Qureshi, Antonio C. de A. Campello, Sueli I. Rodrigues Costa
- IEEE Transactions on Information Theory
- 2018

The Golomb-Welch conjecture (1968) on the non-existence of perfect Lee codes in <inline-formula> <tex-math notation="LaTeX">$\mathbb {Z}^{n}$ </tex-math></inline-formula> with radius <inline-formula>â€¦ (More)

- Sueli I. Rodrigues Costa, Antonio C. de A. Campello, Grasiele C. Jorge, JoÃ£o Strapasson, Claudio Qureshi
- 2014 Information Theory and Applications Workshopâ€¦
- 2014

Codes and associated lattices are studied in the l<sub>p</sub> metric, particularly in the l<sub>1</sub> (Lee) and the l<sub>âˆž</sub> (maximum) distances. Discussions and results on decodingâ€¦ (More)

- Claudio Qureshi, Sueli I. Rodrigues Costa
- 2016 Information Theory and Applications Workshopâ€¦
- 2016

Perfect codes in a given metric are the ones which attain the sphere packing bound. In the Hamming metric perfect linear codes over finite fields are known only to exist for a restricted number ofâ€¦ (More)

- Claudio Qureshi
- ArXiv
- 2018

The Golomb-Welch conjecture states that there are no perfect e-error-correcting Lee codes in Z (PL(n, e)-codes) whenever n â‰¥ 3 and e â‰¥ 2. A special case of this conjecture is when e = 2. In a recentâ€¦ (More)

- Claudio Qureshi, Daniel Panario, Rodrigo Martins
- Adv. in Math. of Comm.
- 2017

- Claudio Qureshi, Daniel Panario
- SIAM J. Discrete Math.
- 2015

We describe the functional graph of the multiplication-by-n map in a cycle group and use this to obtain the structure of the functional graph associated with a RÃ©dei function over a nonbinary finiteâ€¦ (More)

- Claudio Qureshi
- ArXiv
- 2018

The Golomb-Welch conjecture (1968) states that there are no e-perfect Lee codes in Zn for n â‰¥ 3 and e â‰¥ 2. This conjecture remains open even for linear codes. A recent result of Zhang and Geâ€¦ (More)

- Claudio Qureshi, Sueli I. Rodrigues Costa, Christiane Buffo Rodrigues, Michael A Firer
- IEEE Transactions on Information Theory
- 2018

We study the problem of characterizing when two memoryless binary asymmetric channels, described by their transition probabilities <inline-formula> <tex-math notation="LaTeX">$(p,q)$â€¦ (More)

Article history: Received 12 December 2015 Received in revised form 16 February 2016 Accepted 17 February 2016 Available online 1 March 2016 The current study extended previous literature that hadâ€¦ (More)

- Claudio Qureshi, Daniel Panario
- ArXiv
- 2018

We completely describe the functional graph associated to iterations of Chebyshev polynomials over finite fields. Then, we use our structural results to obtain estimates for the average rho length,â€¦ (More)