DocumentCode
1523509
Title
Reed-Muller codes: projections onto GF(4) and multilevel construction
Author
Amrani, Ofer ; Be´ery, Y.
Author_Institution
Dept. of Electr. Eng.-Syst., Tel Aviv Univ., Israel
Volume
47
Issue
6
fYear
2001
fDate
9/1/2001 12:00:00 AM
Firstpage
2560
Lastpage
2565
Abstract
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
Keywords
Galois fields; Reed-Muller codes; binary codes; linear codes; GF(4); Reed-Muller codes; binary codes; code dimension; code length; linear quaternary code; minimum distance; multilevel construction; projections; Binary codes; Block codes; Conferences; Iterative decoding; Lattices; Linear code; Maximum likelihood decoding; Product codes; Turbo codes;
fLanguage
English
Journal_Title
Information Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9448
Type
jour
DOI
10.1109/18.945270
Filename
945270
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