List Decoding of Matrix-Product Codes from nested codes: an application to Quasi-Cyclic codes

Fernando Hernando; Tom Høholdt; Diego Ruano

doi:10.3934/amc.2012.6.259

List Decoding of Matrix-Product Codes from nested codes: an application to Quasi-Cyclic codes

Fernando Hernando
, Tom Høholdt
, Diego Ruano

Jaume I University

Research output: Contribution to journal › Journal article › Research › peer-review

665 Downloads (Orbit)

Abstract

A list decoding algorithm for matrix-product codes is provided when $C_1,..., C_s$ are nested linear codes and $A$ is a non-singular by columns matrix. We estimate the probability of getting more than one codeword as output when the constituent codes are Reed-Solomon codes. We extend this list decoding algorithm for matrix-product codes with polynomial units, which are quasi-cyclic codes. Furthermore, it allows us to consider unique decoding for matrix-product codes with polynomial units.

Original language	English
Journal	Advances in Mathematics of Communication
Volume	6
Issue number	3
Pages (from-to)	259-272
ISSN	1930-5346
DOIs	https://doi.org/10.3934/amc.2012.6.259
Publication status	Published - 2012

Access to Document

10.3934/amc.2012.6.259

F2D46d01Submitted manuscript, 226 KB

OpenUrl availability

Check availability in DTU Findit

Cite this

@article{214e1ce9284448dfa5224bd6ab200c5a,

title = "List Decoding of Matrix-Product Codes from nested codes: an application to Quasi-Cyclic codes",

abstract = "A list decoding algorithm for matrix-product codes is provided when \$C\_1,..., C\_s\$ are nested linear codes and \$A\$ is a non-singular by columns matrix. We estimate the probability of getting more than one codeword as output when the constituent codes are Reed-Solomon codes. We extend this list decoding algorithm for matrix-product codes with polynomial units, which are quasi-cyclic codes. Furthermore, it allows us to consider unique decoding for matrix-product codes with polynomial units.",

author = "Fernando Hernando and Tom H{\o}holdt and Diego Ruano",

year = "2012",

doi = "10.3934/amc.2012.6.259",

language = "English",

volume = "6",

pages = "259--272",

journal = "Advances in Mathematics of Communication",

issn = "1930-5346",

publisher = "American Institute of Mathematical Sciences",

number = "3",

}

TY - JOUR

T1 - List Decoding of Matrix-Product Codes from nested codes: an application to Quasi-Cyclic codes

AU - Hernando, Fernando

AU - Høholdt, Tom

AU - Ruano , Diego

PY - 2012

Y1 - 2012

N2 - A list decoding algorithm for matrix-product codes is provided when $C_1,..., C_s$ are nested linear codes and $A$ is a non-singular by columns matrix. We estimate the probability of getting more than one codeword as output when the constituent codes are Reed-Solomon codes. We extend this list decoding algorithm for matrix-product codes with polynomial units, which are quasi-cyclic codes. Furthermore, it allows us to consider unique decoding for matrix-product codes with polynomial units.

AB - A list decoding algorithm for matrix-product codes is provided when $C_1,..., C_s$ are nested linear codes and $A$ is a non-singular by columns matrix. We estimate the probability of getting more than one codeword as output when the constituent codes are Reed-Solomon codes. We extend this list decoding algorithm for matrix-product codes with polynomial units, which are quasi-cyclic codes. Furthermore, it allows us to consider unique decoding for matrix-product codes with polynomial units.

U2 - 10.3934/amc.2012.6.259

DO - 10.3934/amc.2012.6.259

M3 - Journal article

SN - 1930-5346

VL - 6

SP - 259

EP - 272

JO - Advances in Mathematics of Communication

JF - Advances in Mathematics of Communication

IS - 3

ER -

List Decoding of Matrix-Product Codes from nested codes: an application to Quasi-Cyclic codes

Abstract

Access to Document

OpenUrl availability

Fingerprint

Cite this