Corpus ID: 58006673

# Linear Network Coding: Effects of Varying the Message Dimension on the Set of Characteristics

@article{Das2019LinearNC,
title={Linear Network Coding: Effects of Varying the Message Dimension on the Set of Characteristics},
author={Niladri Das and Brijesh Kumar Rai},
journal={ArXiv},
year={2019},
volume={abs/1901.04820}
}
• Published 15 January 2019
• Computer Science, Mathematics
• ArXiv
It is known a vector linear solution may exist if and only if the characteristic of the finite field belongs to a certain set of primes. But, can increasing the message dimension make a network vector linearly solvable over a larger set of characteristics? To the best of our knowledge, there exists no network in the literature which has a vector linear solution for some message dimension if and only if the characteristic of the finite field belongs to a set $P$, and for some other message… Expand
1 Citations

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#### References

SHOWING 1-10 OF 35 REFERENCES
Insufficiency of linear coding in network information flow
• Mathematics, Computer Science
• IEEE Transactions on Information Theory
• 2005
It is known that every solvable multicast network has a scalar linear solution over a sufficiently large finite-field alphabet. It is also known that this result does not generalize to arbitraryExpand
On the Power of Vector Linear Network Coding
• Mathematics, Computer Science
• 2018 International Symposium on Information Theory and Its Applications (ISITA)
• 2018
This paper presents yet another instance of the power of vector linear network coding over scalar linear network coding. Previous works have established that the size of the finite field required toExpand
On the Message Dimensions of Vector Linearly Solvable Networks
• Mathematics, Computer Science
• IEEE Communications Letters
• 2016
It is known that there exists a network which does not have a scalar linear solution over any finite field but has a vector linear solution when message dimension is 2. It is not known whether thisExpand
On vector linear solvability of multicast networks
• Computer Science
• ICC
• 2015
In the literature of network coding, vector linear network coding (LNC) is a generalization of the conventional scalar LNC, such that the data unit transmitted on every edge is an L-dimensionalExpand
On vector linear solvability of multicast networks
• Computer Science
• ICC
• 2015
In the literature of network coding, vector linear network coding (LNC) is a generalization of the conventional scalar LNC, such that the data unit transmitted on every edge is an L-dimensionalExpand
Linear Network Coding Over Rings – Part II: Vector Codes and Non-Commutative Alphabets
• Mathematics, Computer Science
• IEEE Transactions on Information Theory
• 2018
In Part I, we studied linear network coding over finite commutative rings and made comparisons to the well-studied case of linear network coding over finite fields. Here, we consider the more generalExpand
On base field of linear network coding
• Mathematics, Computer Science
• NetCod
• 2015
A few (single-source) multicast networks were recently discovered with the special property of linearly solvable over a finite field GF(q) but not over a larger GF(q′). In this paper, these networksExpand
On base field of linear network coding
• Mathematics, Computer Science
• NetCod
• 2015
A few (single-source) multicast networks were recently discovered with the special property of linearly solvable over a finite field GF(q) but not over a larger GF(q′). In this paper, these networksExpand
Linear Network Codes and Systems of Polynomial Equations
• Mathematics, Computer Science
• IEEE Transactions on Information Theory
• 2008
If beta and gamma are nonnegative integers and F is a field, then a polynomial collection {p1,hellip ,Pbeta} sube Z[alpha1,hellip, alphagamma] is said to be solvable over F if there existExpand
Vector Linear Solution iff Dimension ≥ m
• Computer Science, Mathematics
• IEEE Commun. Lett.
• 2019
If a network has an $m$ -dimensional vector linear network coding (VLNC) solution, then it also has a VLNC solution for all dimensions multiple of $m$ ; but can a VLNC solution exists for dimensionsExpand