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
Link To Document :
