Optimal quantum codes from additive skew cyclic codes

2016 ◽  
Vol 08 (03) ◽  
pp. 1650037 ◽  
Author(s):  
Nuh Aydin ◽  
Taher Abualrub
Keyword(s):  
Structural Properties ◽  
Cyclic Codes ◽  
The Other ◽  
Quantum Codes ◽  
Additive Codes ◽  
Other Hand ◽  
Skew Cyclic Codes

Additive codes received much attention due to their connections with quantum codes. On the other hand, skew cyclic codes proved to be a useful class of codes that contain many good codes. In this work, we introduce and study additive skew cyclic codes over the quaternary field [Formula: see text], obtaining some structural properties of these codes. Moreover, we also show that many best known and optimal quantum codes can be obtained from this class.

String Generation by Cellular Automata

2021 ◽  
Vol 30 (2) ◽  
pp. 111-132
Author(s):  
Martin Kutrib ◽  
◽  
Andreas Malcher ◽  
Keyword(s):  
Cellular Automata ◽  
Real Time ◽  
Structural Properties ◽  
The Other ◽  
Time Constraints ◽  
Closure Properties ◽  
Other Hand ◽  
The One

In contrast to many investigations of cellular automata with regard to their ability to accept inputs under certain time constraints, in this paper we are studying cellular automata with regard to their ability to generate strings in real time. Structural properties such as speedup results and closure properties are investigated. On the one hand, constructions for the closure under intersection, reversal and length-preserving homomorphism are presented, whereas on the other hand the nonclosure under union, complementation and arbitrary homomorphism are obtained. Finally, decidability questions such as emptiness, finiteness, equivalence, inclusion, regularity and context-freeness are addressed.

Models with the ω-property

1989 ◽  
Vol 54 (1) ◽  
pp. 177-189 ◽  
Author(s):  
Roman Kossak
Keyword(s):  
Structural Properties ◽  
Interesting Property ◽  
Order Type ◽  
Countable Model ◽  
The Other ◽  
Recursive Saturation ◽  
Saturated Models ◽  
Other Hand ◽  
To Come ◽  
Recursively Saturated

In [KP] we have studied the problem of determining when a subset of a (countable) model M of PA can be coded in an elementary end extension of M. Sets with this property are called elementary extensional. In particular we can ask whether there are elementary extensional subsets of a model which have order type ω. It turns out that having elementary extensional subsets of order type ω is an interesting property connected with other structural properties of models of PA. We will call this property the ω-property. In [KP] the problem of characterizing models with the ω-property was left open. It is still open, and the aim of this paper is to present a collection of results pertaining to it. It should be mentioned that the same notion was studied by Kaufmann and Schmerl in [KS2] in connection with some weak notions of saturation which they discuss there. Our notion of a model with the ω-property corresponds to the notion of an upward monotonically ω-lofty cut.It is fairly easy to see that countable recursively saturated models (or in fact all recursively saturated models with cofinality ω) and all short recursively saturated models have the ω-property (Proposition 1.2 below). On the other hand, if we had asked the question about the existence of models with the ω-property before 1975 (when recursively saturated models were introduced) the answer would probably not have been that easy and we would have to come to notions close to recursive saturation.

Skew quasi cyclic codes over 𝔽q + v𝔽q

2019 ◽  
Vol 18 (04) ◽  
pp. 1950077 ◽  
Author(s):  
Mehmet Özen ◽  
N. Tuğba Özzaim ◽  
Halit İnce
Keyword(s):  
Cyclic Codes ◽  
Quantum Codes ◽  
Computer Search ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Generating Set ◽  
Skew Cyclic Codes ◽  
Necessary And Sufficient ◽  
Quantum Parameters ◽  
Quasi Cyclic Codes

In this work, skew quasi cyclic codes over [Formula: see text], where [Formula: see text] are considered. The generating set for one generator skew quasi cyclic codes over [Formula: see text] is also determined. We discuss a sufficient condition for one generator skew quasi cyclic codes to be free. Furthermore, a BCH type bound is given for free one generator skew quasi cyclic codes. We investigate the dual of skew quasi cyclic codes over [Formula: see text]. We give a necessary and sufficient condition for skew cyclic codes over [Formula: see text] to contain its dual. Moreover, we construct quantum codes from skew cyclic codes over [Formula: see text]. By using computer search we give some examples about skew quasi cyclic codes and list some quantum parameters in the table.

scholarly journals Структура и магнетизм сверхрешеток Co/Dy

2020 ◽  
Vol 62 (9) ◽  
pp. 1499
Author(s):  
М.В. Макарова ◽  
Е.А. Кравцов ◽  
В.В. Проглядо ◽  
Yu. Khaydukov ◽  
В.В. Устинов
Keyword(s):  
Magnetic Anisotropy ◽  
Structural Properties ◽  
Perpendicular Magnetic Anisotropy ◽  
The Other ◽  
Periodic Change ◽  
Sample Plane ◽  
Perpendicular Orientation ◽  
Other Hand ◽  
The One

The influence of structural properties on the formation of perpendicular magnetic anisotropy in Co/Dy superlattices is investigated. It is established that superlattices are a compositionally modulated alloy in which, on the one hand, a strict periodicity is maintained in the thickness and composition of the layers, and on the other hand, the interdiffusion of Co and Dy at the interlayer boundaries leads to a periodic change with the depth of the concentration of Co and Dy. It is shown that the perpendicular magnetic anisotropy in Co/Dy is due to the perpendicular orientation of the magnetization in the alloying CoDy layers, while the magnetization of the Co layers is oriented in the sample plane.

On skew cyclic codes over a semi-local ring

2015 ◽  
Vol 07 (04) ◽  
pp. 1550042 ◽  
Author(s):  
Mohammad Ashraf ◽  
Ghulam Mohammad
Keyword(s):  
Local Ring ◽  
Structural Properties ◽  
Decomposition Method ◽  
Cyclic Code ◽  
Cyclic Codes ◽  
Gray Map ◽  
Gray Image ◽  
Skew Cyclic Codes

In the present paper, we study skew cyclic codes over the finite semi-local ring [Formula: see text], where [Formula: see text] and [Formula: see text] is an odd prime. We define a Gray map from [Formula: see text] to [Formula: see text] and investigate the structural properties of skew cyclic codes over [Formula: see text] using decomposition method. It is proved that the Gray image of a skew cyclic code of length [Formula: see text] over [Formula: see text] is a skew [Formula: see text]-quasi-cyclic code of length [Formula: see text] over [Formula: see text]. Further, it is shown that the skew cyclic codes over [Formula: see text] are principally generated.

Skew cyclic codes over Fq + uFq + vFq

2018 ◽  
Vol 11 (05) ◽  
pp. 1850072 ◽  
Author(s):  
Mohammad Ashraf ◽  
Ghulam Mohammad
Keyword(s):  
Structural Properties ◽  
Decomposition Method ◽  
Cyclic Codes ◽  
Gray Map ◽  
Skew Cyclic Codes ◽  
Quasi Cyclic Codes

In this paper, we study skew cyclic codes over the ring [Formula: see text], where [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] is a prime. We define a Gray map from [Formula: see text] to [Formula: see text] and investigate the structural properties of skew cyclic codes over [Formula: see text] using decomposition method. It is shown that the Gray images of skew cyclic codes of length [Formula: see text] over [Formula: see text] are the skew [Formula: see text]-quasi cyclic codes of length [Formula: see text] over [Formula: see text]. Finally, the idempotent generators of skew cyclic codes over [Formula: see text] have also been discussed.

scholarly journals From skew-cyclic codes to asymmetric quantum codes

2011 ◽  
Vol 5 (1) ◽  
pp. 41-57 ◽  
Author(s):  
Martianus Frederic Ezerman ◽  
◽  
San Ling ◽  
Patrick Solé ◽  
Olfa Yemen ◽  
...  
Keyword(s):  
Cyclic Codes ◽  
Quantum Codes ◽  
Asymmetric Quantum ◽  
Asymmetric Quantum Codes ◽  
Skew Cyclic Codes

A class of skew cyclic codes and application in quantum codes construction

2021 ◽  
Vol 344 (2) ◽  
pp. 112189
Author(s):  
Hai Q. Dinh ◽  
Tushar Bag ◽  
Ashish K. Upadhyay ◽  
Ramakrishna Bandi ◽  
Roengchai Tansuchat
Keyword(s):  
Cyclic Codes ◽  
Quantum Codes ◽  
Skew Cyclic Codes
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