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

Publication: Research - peer-reviewJournal article – Annual report year: 2012

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List Decoding of Matrix-Product Codes from nested codes: an application to Quasi-Cyclic codes. / Hernando, Fernando; Høholdt, Tom; Ruano , Diego.

In: Advances in Mathematics of Communication, Vol. 6, No. 3, 2012, p. 259-272.

Publication: Research - peer-reviewJournal article – Annual report year: 2012

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Author

Hernando, Fernando; Høholdt, Tom; Ruano , Diego / List Decoding of Matrix-Product Codes from nested codes: an application to Quasi-Cyclic codes.

In: Advances in Mathematics of Communication, Vol. 6, No. 3, 2012, p. 259-272.

Publication: Research - peer-reviewJournal article – Annual report year: 2012

Bibtex

@article{214e1ce9284448dfa5224bd6ab200c5a,
title = "List Decoding of Matrix-Product Codes from nested codes: an application to Quasi-Cyclic codes",
publisher = "American Institute of Mathematical Sciences",
author = "Fernando Hernando and Tom Høholdt and Diego Ruano",
year = "2012",
doi = "10.3934/amc.2012.6.259",
volume = "6",
number = "3",
pages = "259--272",
journal = "Advances in Mathematics of Communication",
issn = "1930-5346",

}

RIS

TY - JOUR

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

A1 - Hernando,Fernando

A1 - Høholdt,Tom

A1 - Ruano ,Diego

AU - Hernando,Fernando

AU - Høholdt,Tom

AU - Ruano ,Diego

PB - American Institute of Mathematical Sciences

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

JO - Advances in Mathematics of Communication

JF - Advances in Mathematics of Communication

SN - 1930-5346

IS - 3

VL - 6

SP - 259

EP - 272

ER -