# Reed-Muller Identification

@article{Spandri2021ReedMullerI, title={Reed-Muller Identification}, author={Mattia Spandri and Roberto Ferrara and Christian Deppe}, journal={ArXiv}, year={2021}, volume={abs/2107.07649} }

Ahlswede and Dueck identification has the potential of exponentially reducing traffic or exponentially increasing rates in applications where a full decoding of the message is not necessary and, instead, a simple verification of the message of interest suffices. However, the proposed constructions can suffer from exponential increase in the computational load at the sender and receiver, rendering these advantages unusable. This has been shown in particular to be the case for a construction…

## References

SHOWING 1-10 OF 14 REFERENCES

Explicit construction of optimal constant-weight codes for identification via channels

- Mathematics, Computer ScienceIEEE Trans. Inf. Theory
- 1993

It is shown that for any nonzero probabilities of missed and false identification, it is possible to transmit exp(exp(nR)) messages with n uses of a noisy channel, where R is as close as desired to the Shannon capacity of the channel.

On Generalized Reed-Muller Codes and Their Relatives

- Mathematics, Computer ScienceInf. Control.
- 1970

The polynomial formulation of generalized ReedMuller codes is somewhat formalized and an extensive study is made of the interrelations between the m- variable approach of Kasami, Lin, and Peterson and the one-variable approach of Mattson and Solomon.

A framework for the design of good watermark identification codes

- Computer Science, EngineeringElectronic Imaging
- 2006

This paper proposes a practical design of codes for the data-hiding and watermark signature verification application and compares the results with current designs in the literature.

New generalizations of the Reed-Muller codes-I: Primitive codes

- Mathematics, Computer ScienceIEEE Trans. Inf. Theory
- 1968

A natural generalization to the nonbinary case is presented, which also includes the Reed-Muller codes and Reed-Solomon codes as special cases and the generator polynomial is characterized and the minimum weight is established.

Identification in the presence of feedback-A discovery of new capacity formulas

- Mathematics, Computer ScienceIEEE Trans. Inf. Theory
- 1989

A study is made of the identification problem in the presence of a noiseless feedback channel, and the second-order capacity C/sub f/ (resp. C/sub F/) for deterministic (resp. randomized) encoding…

Identification via channels

- Mathematics, Computer ScienceIEEE Trans. Inf. Theory
- 1989

The authors' main finding is that any object among doubly exponentially many objects can be identified in blocklength n with arbitrarily small error probability via a discrete memoryless channel…

Polynomial weights and code constructions

- Mathematics, Computer ScienceIEEE Trans. Inf. Theory
- 1973

It is shown that the polynomials (x - c)^i, i = 0,1,2,\cdots, have the "weight-retaining" property that any linear combination of these polynmials with coefficients in GF(q) has Hamming weight at least as great as that of the minimum degree polynomial included.

IEEE TRANSACTIONS ON INFORMATION THEORY

- 1998

Since at most T of these equations can come from (7), at least (m T) of them come from (8’). Thus, for the distribution (PI’, . . . , p,‘), at most T of the probabilities are nonzero. The proof of…

Information and Control

- Nature
- 1957

It is shown that £t(1)[~(l)] coincides with the class of context-free languages [regular sets] and that ~9' is a proper subset of the family of languages accepted by deterministic linear bounded…