scholarly journals On the Covering Radius of Codes over Z p k

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 328
Author(s):  
Mohan Cruz ◽  
Chinnapillai Durairajan ◽  
Patrick Solé
Keyword(s):  
Upper Bounds ◽  
Covering Radius ◽  
Lower And Upper Bounds ◽  
Zero Divisors ◽  
Lee Distance

In this correspondence, we investigate the covering radius of various types of repetition codes over Z p k ( k ≥ 2 ) with respect to the Lee distance. We determine the exact covering radius of the various repetition codes, which have been constructed using the zero divisors and units in Z p k . We also derive the lower and upper bounds on the covering radius of block repetition codes over Z p k .

On codes over ℤp2 and its covering radius

2019 ◽  
Vol 12 (02) ◽  
pp. 1950027 ◽  
Author(s):  
N. Annamalai ◽  
C. Durairajan
Keyword(s):  
Upper Bounds ◽  
Covering Radius ◽  
Lower And Upper Bounds ◽  
Lee Distance

This paper gives lower and upper bounds on the covering radius of codes over [Formula: see text] with respect to Lee distance. We also determine the covering radius of various repetition codes over [Formula: see text]

On covering radius of codes over ℤ2p

2018 ◽  
Vol 13 (02) ◽  
pp. 2050033 ◽  
Author(s):  
N. Annamalai ◽  
C. Durairajan
Keyword(s):  
Upper Bounds ◽  
Covering Radius ◽  
Lower And Upper Bounds ◽  
Prime Integer ◽  
Lee Distance

In this paper, we gives lower and upper bounds on the covering radius of codes over [Formula: see text], where [Formula: see text] is a prime integer with respect to Lee distance. We also determine the covering radius of various Repetition codes over [Formula: see text], where [Formula: see text] is a prime integer.

scholarly journals Integer Points in Knapsack Polytopes and $s$-Covering Radius

10.37236/2887 ◽  
2013 ◽  
Vol 20 (2) ◽  
Author(s):  
Iskander Aliev ◽  
Martin Henk ◽  
Eva Linke
Keyword(s):  
Lower Bound ◽  
Positive Integer ◽  
Upper Bounds ◽  
Covering Radius ◽  
Frobenius Number ◽  
Lower And Upper Bounds ◽  
Integer Points ◽  
Knapsack Polytope ◽  
Optimal Lower Bound

Given a matrix $A\in \mathbb{Z}^{m\times n}$ satisfying certain regularity assumptions, we consider for a positive integer $s$ the set ${\mathcal F}_s(A)\subset \mathbb{Z}^m$ of all vectors $b\in \mathbb{Z}^m$ such that the associated knapsack polytope\begin{equation*}P(A, b)=\{ x \in \mathbb{R}^n_{\ge 0}: A x= b\}\end{equation*}contains at least $s$ integer points. We present lower and upper bounds on the so called diagonal $s$-Frobenius number associated to the set ${\mathcal F}_s(A)$. In the case $m=1$ we prove an optimal lower bound for the $s$-Frobenius number, which is the largest integer $b$ such that $P(A,b)$ contains less than $s$ integer points.  

On covering radius of codes over R = ℤ2 + uℤ2, where u2 = 0 using chinese euclidean distance

2017 ◽  
Vol 09 (02) ◽  
pp. 1750017 ◽  
Author(s):  
P. Chella Pandian
Keyword(s):  
Euclidean Distance ◽  
Upper Bounds ◽  
Covering Radius ◽  
Lower And Upper Bounds ◽  
Text Type ◽  
Simplex Codes ◽  
Type Code

In this paper, we give lower and upper bounds on the covering radius of codes over the ring [Formula: see text] where [Formula: see text] with respect to Chinese Euclidean distance and also obtain the covering radius of various Repetition codes, Simplex codes of [Formula: see text]-Type code and [Formula: see text]-Type code. We give bounds on the covering radius for MacDonald codes of both types over [Formula: see text]

scholarly journals On codes over the finite non chain ring A = F4+vF4; v2 = v and its covering radius of codes with Bachoc weight

2019 ◽  
Vol 8 (1-2) ◽  
pp. 12-18
Author(s):  
P Chella Pandian
Keyword(s):  
Upper Bounds ◽  
Covering Radius ◽  
Lower And Upper Bounds ◽  
Chain Ring

In this paper, some lower and upper bounds on the covering radius of codes over the nite non chain ring A = F4 + vF4; v2 = v with respect to Bachoc weight is given. Also, the covering radius of various Block Repetition Codes of same and different length over the nite non chain ring A = F4 + vF4; v2 = v is obtained.In this paper, some lower and upper bounds on the covering radius of codes over the nite non chain ring A = F4 + vF4; v2 = v with respect to Bachoc weight is given. Also, the covering radius of various Block Repetition Codes of same and different length over the nite non chain ring A = F4 + vF4; v2 = v is obtained.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

Energy of spherical fuzzy graphs

2020 ◽  
pp. 321-332
Author(s):  
S. Yahya Mohamed ◽  
A. Mohamed Ali
Keyword(s):  
Adjacency Matrix ◽  
Upper Bounds ◽  
Fuzzy Graph ◽  
Lower And Upper Bounds ◽  
Fuzzy Graphs

In this paper, the notion of energy extended to spherical fuzzy graph. The adjacency matrix of a spherical fuzzy graph is defined and we compute the energy of a spherical fuzzy graph as the sum of absolute values of eigenvalues of the adjacency matrix of the spherical fuzzy graph. Also, the lower and upper bounds for the energy of spherical fuzzy graphs are obtained.

scholarly journals Relationship between Age and Value of Information for a Noisy Ornstein–Uhlenbeck Process

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 940
Author(s):  
Zijing Wang ◽  
Mihai-Alin Badiu ◽  
Justin P. Coon
Keyword(s):  
Value Of Information ◽  
Markov Models ◽  
Upper Bounds ◽  
Distribution Functions ◽  
Lower And Upper Bounds ◽  
Uhlenbeck Process ◽  
Source Data ◽  
Non Linear ◽  
Queue Model ◽  
Selection Of

The age of information (AoI) has been widely used to quantify the information freshness in real-time status update systems. As the AoI is independent of the inherent property of the source data and the context, we introduce a mutual information-based value of information (VoI) framework for hidden Markov models. In this paper, we investigate the VoI and its relationship to the AoI for a noisy Ornstein–Uhlenbeck (OU) process. We explore the effects of correlation and noise on their relationship, and find logarithmic, exponential and linear dependencies between the two in three different regimes. This gives the formal justification for the selection of non-linear AoI functions previously reported in other works. Moreover, we study the statistical properties of the VoI in the example of a queue model, deriving its distribution functions and moments. The lower and upper bounds of the average VoI are also analysed, which can be used for the design and optimisation of freshness-aware networks. Numerical results are presented and further show that, compared with the traditional linear age and some basic non-linear age functions, the proposed VoI framework is more general and suitable for various contexts.

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