TY - JOUR
T1 - Reed-muller codes and Barnes-Wall lattices
T2 - Generalized multilevel constructions and representation over GF(2 q)
AU - Salomon, Amir J.
AU - Amrani, Ofer
PY - 2007/1
Y1 - 2007/1
N2 - Generalized multilevel constructions for binary RM(r,m) codes using projections onto GF(2 q ) are presented. These constructions exploit component codes over GF(2), GF(4),..., GF(2 q ) that are based on shorter Reed-Muller codes and set partitioning using partition chains of length-2 l codes. Using these constructions we derive multilevel constructions for the Barnes-Wall Λ(r,m) family of lattices which also use component codes over GF(2), GF(4),..., GF(2 q ) and set partitioning based on partition chains of length-2 l lattices. These constructions of Reed-Muller codes and Barnes-Wall lattices are readily applicable for their efficient decoding.
AB - Generalized multilevel constructions for binary RM(r,m) codes using projections onto GF(2 q ) are presented. These constructions exploit component codes over GF(2), GF(4),..., GF(2 q ) that are based on shorter Reed-Muller codes and set partitioning using partition chains of length-2 l codes. Using these constructions we derive multilevel constructions for the Barnes-Wall Λ(r,m) family of lattices which also use component codes over GF(2), GF(4),..., GF(2 q ) and set partitioning based on partition chains of length-2 l lattices. These constructions of Reed-Muller codes and Barnes-Wall lattices are readily applicable for their efficient decoding.
KW - Additive codes
KW - Barnes-Wall lattices
KW - Finite-fields
KW - Mapping
KW - Multilevel
KW - Multistage
KW - Projection
KW - Reed-Muller codes
KW - Set partition
UR - http://www.scopus.com/inward/record.url?scp=33846245556&partnerID=8YFLogxK
U2 - 10.1007/s10623-006-9028-3
DO - 10.1007/s10623-006-9028-3
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AN - SCOPUS:33846245556
SN - 0925-1022
VL - 42
SP - 167
EP - 180
JO - Designs, Codes, and Cryptography
JF - Designs, Codes, and Cryptography
IS - 2
ER -