196,154 research outputs found
Skew-cyclic codes
We generalize the notion of cyclic codes by using generator polynomials in
(non commutative) skew polynomial rings. Since skew polynomial rings are left
and right euclidean, the obtained codes share most properties of cyclic codes.
Since there are much more skew-cyclic codes, this new class of codes allows to
systematically search for codes with good properties. We give many examples of
codes which improve the previously best known linear codes
The Permutation Groups and the Equivalence of Cyclic and Quasi-Cyclic Codes
We give the class of finite groups which arise as the permutation groups of
cyclic codes over finite fields. Furthermore, we extend the results of Brand
and Huffman et al. and we find the properties of the set of permutations by
which two cyclic codes of length p^r can be equivalent. We also find the set of
permutations by which two quasi-cyclic codes can be equivalent
Transitive and self-dual codes attaining the Tsfasman-Vladut-Zink bound
A major problem in coding theory is the question of whether the class of cyclic codes is asymptotically good. In this correspondence-as a generalization of cyclic codes-the notion of transitive codes is introduced (see Definition 1.4 in Section I), and it is shown that the class of transitive codes is asymptotically good. Even more, transitive codes attain the Tsfasman-Vladut-Zink bound over F-q, for all squares q = l(2). It is also shown that self-orthogonal and self-dual codes attain the Tsfasman-Vladut-Zink bound, thus improving previous results about self-dual codes attaining the Gilbert-Varshamov bound. The main tool is a new asymptotically optimal tower E-0 subset of E-1 subset of E-2 subset of center dot center dot center dot of function fields over F-q (with q = l(2)), where all extensions E-n/E-0 are Galois
Resilience to time-correlated noise in quantum computation
Fault-tolerant quantum computation techniques rely on weakly correlated
noise. Here I show that it is enough to assume weak spatial correlations: time
correlations can take any form. In particular, single-shot error correction
techniques exhibit a noise threshold for quantum memories under spatially local
stochastic noise.Comment: 16 pages, v3: as accepted in journa
- …