Results 11 to 20 of about 5,176 (95)

Quantum computation from dynamic automorphism codes [PDF]

Quantum
We propose a new model of quantum computation comprised of low-weight measurement sequences that simultaneously encode logical information, enable error correction, and apply logical gates.
Margarita Davydova, Nathanan Tantivasadakarn, Shankar Balasubramanian, David Aasen   +3 more
doaj   +1 more source

Support Constrained Generator Matrices of Gabidulin Codes in Characteristic Zero [PDF]

, 2020
Gabidulin codes over fields of characteristic zero were recently constructed by Augot et al., whenever the Galois group of the underlying field extension is cyclic.
Hassibi, Babak, Raviv, Netanel, Yildiz, Hikmet   +2 more
core   +2 more sources

On extremal self-dual ternary codes of length 48 [PDF]

, 2011
All extremal ternary codes of length 48 that have some automorphism of prime order $p\geq 5$ are equivalent to one of the two known codes, the Pless code or the extended quadratic residue ...
Nebe, Gabriele
core   +4 more sources

On the Equivalence of Quadratic APN Functions [PDF]

, 2010
Establishing the CCZ-equivalence of a pair of APN functions is generally quite difficult. In some cases, when seeking to show that a putative new infinite family of APN functions is CCZ inequivalent to an already known family, we rely on computer ...
C. Bracken, Carl Bracken, E. Byrne, Eimear Byrne Gary, G. Mcguire, G. Nebe, Mcguire Gabriele Nebe   +6 more
core   +3 more sources

Automorphism groups of Grassmann codes

, 2013
We use a theorem of Chow (1949) on line-preserving bijections of Grassmannians to determine the automorphism group of Grassmann codes. Further, we analyze the automorphisms of the big cell of a Grassmannian and then use it to settle an open question of ...
Artin, Beelen, Beelen, Berger, Bogart, Chow, Ghorpade, Ghorpade, Griffiths, Harris, Hirschfeld, Hodge, Krishna V. Kaipa, Lakshmibai, MacWilliams, Nemitz, Nogin, Pankov, Prażmowski, Sudhir R. Ghorpade, Tsfasman, Tsfasman, Wan, Ward, Westwick   +24 more
core   +2 more sources

Diagonally Neighbour Transitive Codes and Frequency Permutation Arrays [PDF]

, 2014
Constant composition codes have been proposed as suitable coding schemes to solve the narrow band and impulse noise problems associated with powerline communication.
A. Neumaier, A.E. Brouwer, Cheryl E. Praeger, D. Slepian, D. Smith, I. Blake, I.F. Blake, J.M. Goethals, M. Giudici, N. Gillespie, N. Pavlidou, Neil I. Gillespie, P. Dukes, P. Frankl, P. Keevash, R.F. Bailey, S. Huczynska, V. Pless, W. Chu, W. Chu   +19 more
core   +4 more sources

Twisted Permutation Codes [PDF]

, 2014
We introduce twisted permutation codes, which are frequency permutation arrays analogous to repetition permutation codes, namely, codes obtained from the repetition construction applied to a permutation code. In particular, we show that a lower bound for
Gillespie, Neil I., Praeger, Cheryl E., Spiga, Pablo   +2 more
core   +4 more sources

Leveraging Automorphisms of Quantum Codes for Fault-Tolerant Quantum Computation

, 2013
Fault-tolerant quantum computation is a technique that is necessary to build a scalable quantum computer from noisy physical building blocks. Key for the implementation of fault-tolerant computations is the ability to perform a universal set of quantum ...
Grassl, Markus, Roetteler, Martin
core   +1 more source

$ (\theta_i, \lambda) $-constacyclic codes and DNA codes over $ \mathbb{Z}_{4}+u\mathbb{Z}_{4}+u^{2}\mathbb{Z}_{4} $

AIMS Mathematics
In this paper, three new automorphisms were identified over the ring $ \mathbb{Z}_{4}+u\mathbb{Z}_{4}+u^{2}\mathbb{Z}_{4} $ where $ u^3 = u^2 $. With the help of these automorphisms, the characteristic structures of the generator polynomials for the ...
Fatma Zehra Uzekmek , Elif Segah Oztas, Mehmet Ozen   +2 more
doaj   +1 more source

Constant 2-Labellings And An Application To (R, A, B)-Covering Codes

Discussiones Mathematicae Graph Theory, 2017
We introduce the concept of constant 2-labelling of a vertex-weighted graph and show how it can be used to obtain perfect weighted coverings. Roughly speaking, a constant 2-labelling of a vertex-weighted graph is a black and white colouring of its vertex
Gravier Sylvain, Vandomme Èlise
doaj   +1 more source