# List-decodable Codes and Covering Codes

@article{Chen2021ListdecodableCA, title={List-decodable Codes and Covering Codes}, author={Hao Chen}, journal={ArXiv}, year={2021}, volume={abs/2109.02818} }

The list-decodable code has been an active topic in theoretical computer science since the seminal papers of M. Sudan and V. Guruswami in 1997-1998. There are general result about the Johnson radius and the list-decoding capacity theorem. However few results about general constraints on rates, list-decodable radius and list sizes for listdecodable codes have been obtained. List-decodable codes are also considered in rank-metric, subspace metric, cover-metric, pair metric and insdel metric…

## One Citation

Upper bounds on the length function for covering codes

- Computer Science, MathematicsAdvances in Mathematics of Communications
- 2022

New upper bounds on `q(tR + 1, R) are obtained in the following forms: q is an arbitrary prime power, c is independent of q, and q is large enough.

## References

SHOWING 1-10 OF 146 REFERENCES

Efficiently List-Decodable Insertion and Deletion Codes via Concatenation

- Computer ScienceIEEE Transactions on Information Theory
- 2021

A family of insdel codes along with their efficient encoding and decoding algorithms through concatenation method is constructed which provides a Zyablov-type bound for insdel metric codes.

A Lower Bound on List Size for List Decoding

- Computer Science, MathematicsIEEE Trans. Inf. Theory
- 2010

It is proved that there exists a constant cq > 0 and a function fq such that for small enough e > 0, if C is list-decodable to radius (1-1/q)(1- e)n with list size cq/ e2, then C has at most fq( e) codewords, independent of n .

Construction and covering properties of constant-dimension codes

- Mathematics, Computer Science2009 IEEE International Symposium on Information Theory
- 2009

A new class of CDCs based on KK codes are constructed, whose cardinalities are greater than previously proposed CDCs, and a low-complexity decoding algorithm is proposed that corrects more errors than a bounded subspace distance decoder by taking advantage of the structure of the authors' augmented KK code.

Combinatorial bounds for list decoding

- Mathematics, Computer ScienceIEEE Trans. Inf. Theory
- 2002

This work presents a polynomial time constructible asymptotically good family of binary codes of rate /spl Omega/(/spl epsi//sup 4/) that can be list-decoded in polynometric time from up to a fraction of errors, using lists of size O(/spl Epsi //sup -2/).

Fundamental Properties of Sum-Rank-Metric Codes

- Computer Science, MathematicsIEEE Transactions on Information Theory
- 2021

This paper investigates the theory of sum-rank-metric codes for which the individual matrix blocks may have different sizes. Various bounds on the cardinality of a code are derived, along with their…

Algebraic List-Decoding in Projective Space: Decoding With Multiplicities and Rank-Metric Codes

- Mathematics, Computer ScienceIEEE Transactions on Information Theory
- 2019

Two separate methods are developed, via two different approaches, for list decoding subspace codes and rank-metric codes that provide improved tradeoffs between rate and error-correction capability and a folded version of Koetter-Kschischang codes is constructed.

List decoding of symbol-pair codes

- IEEE Transactions on Information Theory,
- 2019

New covering codes of radius R, codimension tR and tR+ R2 , and saturating sets in projective spaces, Designs, codes and cryptography

- 2019

On List Decoding of Insertion and Deletion Errors

- Computer Science, MathematicsArXiv
- 2019

An upper bound on the list decoding radius of an insdel code in terms of its rate is provided and a Zyablov-type bound for insdel errors is obtained and a family of explicit insdel codes is constructed with efficient list decoding algorithm.

Optimally resilient codes for list-decoding from insertions and deletions

- Computer Science, MathematicsElectron. Colloquium Comput. Complex.
- 2019

The main technical work in the results is proving the existence of code families of sufficiently large size with good list-decoding properties for any combination of δ,γ within the claimed feasibility region.