3,512 research outputs found
Non-commutative Geometry Modified Non-Gaussianities of Cosmological Perturbation
We investigate the noncommutative effect on the non-Gaussianities of
primordial cosmological perturbation. In the lowest order of string length and
slow-roll parameter, we find that in the models with small speed of sound the
noncommutative modifications could be observable if assuming a relatively low
string scale. In particular, the dominant modification of non-Gaussianity
estimator f_{NL} could reach O(1) in DBI inflation and K-inflation. The
corrections are sensitive to the speed of sound and the choice of string length
scale. Moreover the shapes of the corrected non-Gaussianities are distinct from
that of ordinary ones.Comment: 26 pages, 3 figures Added references, changed conten
Singleton-Optimal LRCs and Perfect LRCs via Cyclic and Constacyclic Codes
Locally repairable codes (LRCs) have emerged as an important coding scheme in
distributed storage systems (DSSs) with relatively low repair cost by accessing
fewer non-failure nodes. Theoretical bounds and optimal constructions of LRCs
have been widely investigated. Optimal LRCs via cyclic and constacyclic codes
provide significant benefit of elegant algebraic structure and efficient
encoding procedure. In this paper, we continue to consider the constructions of
optimal LRCs via cyclic and constacyclic codes with long code length.
Specifically, we first obtain two classes of -ary cyclic Singleton-optimal
-LRCs with length when and is
even, and length when and , respectively. To the best of our knowledge, this is the first
construction of -ary cyclic Singleton-optimal LRCs with length and
minimum distance . On the other hand, an LRC acheiving the
Hamming-type bound is called a perfect LRC. By using cyclic and constacyclic
codes, we construct two new families of -ary perfect LRCs with length
, minimum distance and locality
Bounds and Constructions of Singleton-Optimal Locally Repairable Codes with Small Localities
Constructions of optimal locally repairable codes (LRCs) achieving
Singleton-type bound have been exhaustively investigated in recent years. In
this paper, we consider new bounds and constructions of Singleton-optimal LRCs
with minmum distance , locality and minimum distance and
locality , respectively. Firstly, we establish equivalent connections
between the existence of these two families of LRCs and the existence of some
subsets of lines in the projective space with certain properties. Then, we
employ the line-point incidence matrix and Johnson bounds for constant weight
codes to derive new improved bounds on the code length, which are tighter than
known results. Finally, by using some techniques of finite field and finite
geometry, we give some new constructions of Singleton-optimal LRCs, which have
larger length than previous ones
Development of Zirconia Nanocomposite Ceramic Tool and Die Material Based on Tribological Design
- β¦