List Decoding of Matrix-Product Codes from nested codes: an application to Quasi-Cyclic codes
Publication: Research - peer-review › Journal 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-review › Journal article – Annual report year: 2012
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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 -