On Base Field of Linear Network Coding

For a (single-source) multicast network, the size of a base field is the most known and studied algebraic identity that is involved in characterizing its linear solvability over the base field. In this paper, we design a new class N of multicast networks and obtain an explicit formula for the linear...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 62; no. 12; pp. 7272 - 7282
Main Authors: Sun, Qifu Tyler, Li, Shuo-Yen Robert, Zongpeng Li
Format: Journal Article
Language:English
Published: New York IEEE 01.12.2016
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algebra
Communications networks
Computers
coset
Cryptography
Electronic mail
Encoding
generalized Cauchy-Davenport theorem
Indexes
multicast network
multiplicative subgroup
Network coding
Receivers
Sun
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary:For a (single-source) multicast network, the size of a base field is the most known and studied algebraic identity that is involved in characterizing its linear solvability over the base field. In this paper, we design a new class N of multicast networks and obtain an explicit formula for the linear solvability of these networks, which involves the associated coset numbers of a multiplicative subgroup in a base field. The concise formula turns out to be the first that matches the topological structure of a multicast network and algebraic identities of a field other than size. It further facilitates us to unveil infinitely many new multicast networks linearly solvable over GF(q) but not over GF(q') with q <; q', based on a subgroup order criterion. In particular: 1) for every k ≥ 2, an instance in N can be found linearly solvable over GF(2 2k ) but not over GF(2 2k+1 ) and 2) for arbitrary distinct primes p and p', there are infinitely many k and k' such that an instance in N can be found linearly solvable over GF(p k ) but not over GF(p' k ') with p k <; p' k' .
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2016.2613988