In 2010, Silva, Kschischang and Kötter studied certain classes of finite field matrix channels in order to model random linear network coding where exactly t random errors are introduced. In this paper we introduce a generalisation of these matrix channels where the number of errors is not required to be constant. We show that a capacity-achieving input distribution can always be taken to have ...

The rate of a network code is the ratio of the block sizes of the network’s messages and its edge codewords. The linear capacity of a network over a finite ring alphabet is the supremum of achievable rates using linear codes over the ring. We prove the following for directed acyclic networks: (i) For every finite field F and every finite ring R, there is some network whose linear capacity over ...

This paper explores the relationships between noncooperative bargaining games and the consistent value for non-transferable utility (NTU) cooperative games. A dynamic approach to the consistent value for NTU games is introduced: the consistent vector field. The main contribution of the paper is to show that the consistent field is intimately related to the concept of subgame perfection for fini...

Finite fields have great applications in various areas as cryptography, that is why it is important to have fast ways of computation to manipulate them. A first approach developed in this report lies in representing integers of the field using floating-point numbers, which lead to efficient computations. Operations in our case are done by restricting the characteristic p of the field to a float...

Finite fields have great applications in various areas as cryptography, that is why it is important to have fast ways of computation to manipulate them. A first approach developed in this report lies in representing integers of the field using floating-point numbers, which lead to efficient computations. Operations in our case are done by restricting the characteristic p of the field to a float...

With the end goal of implementing optimal Reed-Solomon error control decoders on FPGAs, we characterize the FPGA performance of several finite field multiplier designs reported in the literature. We discover that finite field multipliers optimized for VLSI implementation are not optimized for FPGA implementation. Based on this observation, we discuss the relative merits of each multiplier desig...

In information security field underlying cryptography, random sequences, which are the base of system security, play a very important role. Random sequences with high security are often needed in cryptography field. From the view of security, real random sequences should be completely unpredictable and reliable. In many circumstances, a random number not only need to be random, but also need to...

The study of many problems in additive combinatorics, such as Szemerédi’s theorem on arithmetic progressions, is made easier by first studying models for the problem in F p , for some fixed small prime p. We give a number of examples of finite field models of this type, which allows us to introduce some of the central ideas in additive combinatorics relatively cleanly. We also give an indicatio...

This article presents simple and highly regular architectures for finite field multipliers using a redundant representation. The basic idea is to embed a finite field into a cyclotomic ring which has a basis with the elegant multiplicative structure of a cyclic group. One important feature of our architectures is that they provide area-time trade-offs which enable us to implement the multiplier...