# On decoding hyperbolic codes

@article{CampsMoreno2021OnDH, title={On decoding hyperbolic codes}, author={Eduardo Camps-Moreno and Ignacio Garc'ia-Marco and H. L'opez and Irene M'arquez-Corbella and E. Mart'inez-Moro and Eliseo Sarmiento}, journal={ArXiv}, year={2021}, volume={abs/2107.12594} }

Few decoding algorithms for hyperbolic codes are known in the literature, this article tries to fill this gap. The first part of this work compares hyperbolic codes and ReedMuller codes. In particular, we determine when a Reed-Muller code is a hyperbolic code. As a byproduct, we state when a hyperbolic code has greater dimension than a Reed-Muller code when they both have the same minimum distance. We use the previous ideas to describe how to decode a hyperbolic code using the largest Reed… Expand

#### References

SHOWING 1-10 OF 30 REFERENCES

Recursive projection-aggregation decoding of Reed-Muller codes

- Computer Science, Mathematics
- 2019 IEEE International Symposium on Information Theory (ISIT)
- 2019

A new class of efficient decoding algorithms for Reed-Muller (RM) codes over binary-input memoryless channels based on projecting the code on its cosets, recursively decoding the projected codes, and aggregating the reconstructions. Expand

List decoding tensor products and interleaved codes

- Computer Science, Mathematics
- STOC '09
- 2009

This work designs the first efficient algorithms and proves new combinatorial bounds for list decoding tensor products of codes and interleaved codes, and gives better bounds on the list decoding radius than what is obtained from the Johnson bound. Expand

Improved decoding of Reed-Solomon and algebraic-geometry codes

- Mathematics, Computer Science
- IEEE Trans. Inf. Theory
- 1999

An improved list decoding algorithm for decoding Reed-Solomon codes and alternant codes and algebraic-geometry codes is presented and a solution to a weighted curve-fitting problem is presented, which may be of use in soft-decision decoding algorithms for Reed- Solomon codes. Expand

Soft-decision decoding of Reed-Muller codes: recursive lists

- Computer Science, Mathematics
- IEEE Transactions on Information Theory
- 2006

Simulation results show that for all RM codes of length 256 and many subcodes of length 512, these algorithms approach maximum-likelihood (ML) performance within a margin of 0.1 dB. Expand

Evaluation codes from order domain theory

- Computer Science, Mathematics
- Finite Fields Their Appl.
- 2008

A simple lower bound on the minimum distance of codes defined by means of their generator matrices is derived and interpreted into the setting of order domain theory to fill in an obvious gap in the theory of order domains. Expand

Theory of Error-correcting Codes

The field of channel coding started with Claude Shannon's 1948 landmark paper. Fifty years of efforts and invention have finally produced coding schemes that closely approach Shannon's channel… Expand

List decoding of q-ary Reed-Muller codes

- Computer Science
- IEEE Transactions on Information Theory
- 2004

This correspondence shows that q-ary RM codes are subfield subcodes of RS codes over F/sub q//sup m/ and presents a list-decoding algorithm, applicable to codes of any rates, and achieves an error-correction bound n(1-/spl radic)/n. Expand

A Method for Solving Key Equation for Decoding Goppa Codes

- Computer Science, Mathematics
- Inf. Control.
- 1975

It is shown that the key equation for decoding Goppa codes can be solved using Euclid's algorithm, and the error locator polynomial is proved the multiplierPolynomial for the syndrome poynomial multiplied by an appropriate scalar factor. Expand

Footprints or generalized Bezout's theorem

- Mathematics, Computer Science
- IEEE Trans. Inf. Theory
- 2000

The main aim of this article is to show that the results and some improvements can be obtained by using the so-called footprint from Grobner basis theory, and develop the theory further such that the minimum distance and the generalized Hamming weights not only can be estimated but also can actually be determined. Expand

Polar Decreasing Monomial-Cartesian Codes

- Computer Science, Mathematics
- IEEE Transactions on Information Theory
- 2021

It is proved that families of polar codes with multiple kernels over certain symmetric channels can be viewed as polar decreasing monomial-Cartesian codes, and this offers a unified treatment for such codes over any finite field. Expand