DocumentCode
912302
Title
Some Remarks on BCH Bounds and Minimum Weights of Binary Primitive BCH Codes
Author
Kasami, Tadao ; Tokura, Nobuki
Volume
15
Issue
3
fYear
1969
fDate
5/1/1969 12:00:00 AM
Firstpage
408
Lastpage
413
Abstract
It is shown that if 
and 
, there are some binary primitive BCH codes (BCH codes in a narrow sense) of length 
whose minimum weight is greater than the BCH bound. This gives a negative answer to the question posed by Peterson [1] of whether or not the BCH bound is always the actual minimum weight of a binary primitive BCH code. It is also shown that for any even 
, there are some binary cyclic codes of length that have more information digits than the primitive BCH codes of length with the same minimum weight.
and , there are some binary primitive BCH codes (BCH codes in a narrow sense) of length whose minimum weight is greater than the BCH bound. This gives a negative answer to the question posed by Peterson [1] of whether or not the BCH bound is always the actual minimum weight of a binary primitive BCH code. It is also shown that for any even , there are some binary cyclic codes of length that have more information digits than the primitive BCH codes of length with the same minimum weight.Keywords
BCH codes; Cathode ray tubes; Parity check codes;
fLanguage
English
Journal_Title
Information Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9448
Type
jour
DOI
10.1109/TIT.1969.1054304
Filename
1054304
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