TY - JOUR
T1 - Reed-Muller codes
T2 - Projections onto GF(4) and multilevel construction
AU - Amrani, Ofer
AU - Be'ery, Yair
PY - 2001/9
Y1 - 2001/9
N2 - A projection of binary Reed-Muller codes R(r, m) onto GF (4) m-2 is presented. For an R(r, m) code, this operation yields a linear quaternary code with the same length, dimension, and minimum distance as the Reed-Muller R(r-1, m-2) code. Based upon this projection, multilevel construction is given for R(r, m), where the constituent codes applied to the different levels are themselves the Reed-Muller codes R(r - 2, m - 2) and R(r, m - 2), as well as the aforementioned quaternary code. This construction of Reed-Muller codes is readily applicable for their efficient decoding.
AB - A projection of binary Reed-Muller codes R(r, m) onto GF (4) m-2 is presented. For an R(r, m) code, this operation yields a linear quaternary code with the same length, dimension, and minimum distance as the Reed-Muller R(r-1, m-2) code. Based upon this projection, multilevel construction is given for R(r, m), where the constituent codes applied to the different levels are themselves the Reed-Muller codes R(r - 2, m - 2) and R(r, m - 2), as well as the aforementioned quaternary code. This construction of Reed-Muller codes is readily applicable for their efficient decoding.
KW - Mapping
KW - Multilevel
KW - Multistage
KW - Projection
KW - Reed-Muller codes
UR - http://www.scopus.com/inward/record.url?scp=0035441848&partnerID=8YFLogxK
U2 - 10.1109/18.945270
DO - 10.1109/18.945270
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AN - SCOPUS:0035441848
SN - 0018-9448
VL - 47
SP - 2560
EP - 2565
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 6
ER -