DocumentCode :
945900
Title :
Maximum-weight group codes for the balanced 
-ary channel
-ary channelAuthor :
Helstrom, Carl W.
Volume :
6
Issue :
5
fYear :
1960
fDate :
12/1/1960 12:00:00 AM
Firstpage :
550
Lastpage :
555
Abstract :
The construction of 
group alphabets is discussed for the balanced -ary channel, where is the power of a prime. In this channel all digits are equally likely to be in error, and an incorrect digit is equally likely to be any digit besides the one sent. The alphabets are formed by taking 
columns of the modular representation table of the Abelian group of 
-tuples of elements from the Galois field 
under digitwise addition. The formation and properties of that table are described. Attention is focused on alphabets in which all letters except the -tuple of O\´s have the maximum number of non-null elements. Tables of such alphabets are given for 
; and 
.
group alphabets is discussed for the balanced -ary channel, where is the power of a prime. In this channel all digits are equally likely to be in error, and an incorrect digit is equally likely to be any digit besides the one sent. The alphabets are formed by taking columns of the modular representation table of the Abelian group of -tuples of elements from the Galois field under digitwise addition. The formation and properties of that table are described. Attention is focused on alphabets in which all letters except the -tuple of O\´s have the maximum number of non-null elements. Tables of such alphabets are given for ; and .Keywords :
Group codes; Bandwidth; Error correction codes; Frequency; Galois fields; Gaussian noise; Information theory; Matched filters; Narrowband; Phase detection; Phase modulation; Random variables; Shape;
fLanguage :
English
Journal_Title :
Information Theory, IRE Transactions on
Publisher :
ieee
ISSN :
0096-1000
Type :
jour
DOI :
10.1109/TIT.1960.1057601
Filename :
1057601
Link To Document :
