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On the optimum bit orders with respect to the state complexity of trellis diagrams for binary linear codesIt was shown earlier that for a punctured Reed-Muller (RM) code or a primitive BCH code, which contains a punctured RM code of the same minimum distance as a large subcode, the state complexity of the minimal trellis diagram is much greater than that for an equivalent code obtained by a proper permutation on the bit positions. To find a permutation on the bit positions for a given code that minimizes the state complexity of its minimal trellis diagram is an interesting and challenging problem. This permutation problem is related to the generalized Hamming weight hierarchy of a code, and is shown that for RM codes, the standard binary order of bit positions is optimum at every bit position with respect to the state complexity of a minimal trellis diagram by using a theorem due to Wei. The state complexity of trellis diagram for the extended and permuted (64, 24) BCH code is discussed.
Document ID
19930048795
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
External Source(s)
Authors
Kasami, Tadao
(NASA Goddard Space Flight Center Greenbelt, MD, United States)
Takata, Toyoo
(NASA Goddard Space Flight Center Greenbelt, MD, United States)
Fujiwara, Toru
(Osaka Univ. Toyonaka, Japan)
Lin, Shu
(Hawaii Univ. Honolulu, United States)
Date Acquired
August 16, 2013
Publication Date
January 1, 1993
Publication Information
Publication: IEEE Transactions on Information Theory
Volume: 39
Issue: 1
ISSN: 0018-9448
Subject Category
Communications And Radar
Accession Number
93A32792
Funding Number(s)
CONTRACT_GRANT: MOESC-63550255
CONTRACT_GRANT: NSF NCR-91-15400
CONTRACT_GRANT: NSF NCR-88-13480
CONTRACT_GRANT: NAG5-931
Distribution Limits
Public
Copyright
Other

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