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We present a general theory to obtain linear network codes utilizing forms and obtain explicit families of equidimensional vector spaces, in which any pair of distinct vector spaces intersect in the same small dimension. The theory is…
Linear network coding transmits information in terms of a basis of a vector space and the information is received as a basis of a possible altered vectorspace. Ralf Koetter and Frank R. Kschischang in Coding for errors and erasures in…
We construct linear network codes utilizing algebraic curves over finite fields and certain associated Riemann-Roch spaces and present methods to obtain their parameters. In particular we treat the Hermitian curve and the curves associated…
The problem of error-control in random linear network coding is considered. A ``noncoherent'' or ``channel oblivious'' model is assumed where neither transmitter nor receiver is assumed to have knowledge of the channel transfer…
This paper considers vector network coding based on rank-metric codes and subspace codes. Our main result is that vector network coding can significantly reduce the required field size compared to scalar linear network coding in the same…
This paper considers vector network coding solutions based on rank-metric codes and subspace codes. The main result of this paper is that vector solutions can significantly reduce the required alphabet size compared to the optimal scalar…
In [1], K\"otter and Kschischang presented a new model for error correcting codes in network coding. The alphabet in this model is the subspace lattice of a given vector space, a code is a subset of this lattice and the used metric on this…
Circular-shift linear network coding (LNC) is a class of vector LNC with local encoding kernels selected from cyclic permutation matrices, so that it has low coding complexities. However, it is insufficient to exactly achieve the capacity…
Grassmannian codes are known to be useful in error-correction for random network coding. Recently, they were used to prove that vector network codes outperform scalar linear network codes, on multicast networks, with respect to the alphabet…
A spread code is a set of vector spaces of a fixed dimension over a finite field Fq with certain properties used for random network coding. It can be constructed in different ways which lead to different decoding algorithms. In this work we…
Basic algebraic and combinatorial properties of finite vector spaces in which individual vectors are allowed to have multiplicities larger than $ 1 $ are derived. An application in coding theory is illustrated by showing that multispace…
The study of linear codes over a finite field of odd cardinality, derived from determinantal varieties obtained from symmetric matrices of bounded rank, was initiated in a recent paper by the authors. There, one found the minimum distance…
Real complex networks are often characterized by spatial constraints such as the relative position and adjacency of nodes. The present work describes how Voronoi tessellations of the space where the network is embedded provide not only a…
Random linear network coding (RLNC) provides a powerful framework for non-coherent communication, where reliable transmission requires correcting errors and erasures induced by network mixing and motivates the use of subspace codes. In this…
This paper investigates the construction of linear network codes for broadcasting a set of data packets to a number of users. The links from the source to the users are modeled as independent erasure channels. Users are allowed to inform…
When two or more users in a wireless network transmit simultaneously, their electromagnetic signals are linearly superimposed on the channel. As a result, a receiver that is interested in one of these signals sees the others as unwanted…
In this paper, we present a coding-theoretic framework for message transmission over packet-switched networks. Network is modeled as a channel which can induce packet errors, deletions, insertions, and out of order delivery of packets. The…
This paper proposes a discrimination technique for vertices in a weighted network. We assume that the edge weights and adjacencies in the network are conditionally independent and that both sources of information encode class membership…
In this work, we introduce convolutional codes for network-error correction in the context of coherent network coding. We give a construction of convolutional codes that correct a given set of error patterns, as long as consecutive errors…
We consider methods for quantifying the similarity of vertices in networks. We propose a measure of similarity based on the concept that two vertices are similar if their immediate neighbors in the network are themselves similar. This leads…