DocumentCode :
918553
Title :
A theory of two-dimensional linear recurring arrays
Author :
Nomura, Tamiya ; Miyakawa, Hiroshi ; Imai, Hideki ; Fukuda, Akira
Volume :
18
Issue :
6
fYear :
1972
fDate :
11/1/1972 12:00:00 AM
Firstpage :
775
Lastpage :
785
Abstract :
In this paper, two-dimensional arrays of elements of an arbitrary finite field are examined, especially arrays having maximum-area matrices. We first define two-dimensional linear recurring arrays. In order to study the characteristics of two-dimensional linear recurring arrays, we also define two-dimensional linear cyclic codes. A systematic method of constructing two-dimensional linear recurring arrays having maximum-area matrices is given using the theory of two-dimensional cyclic codes. These arrays, here called \\gamma \\beta -arrays, may be said to be two-dimensional analogs of M -sequences. A \\gamma \\beta -array of area N_x \\times N_y exists over GF(q) if and only if N_x N_y is equal to q^N _ 1 for some positive integer N . Many interesting characteristics of the \\gamma \\beta -array, such as the properties of its autocorrelation function and the properties of the characteristic arrays, are deduced and explained.
Keywords :
Cyclic codes; Matrices; Multidimensional codes; Autocorrelation; Galois fields; Helium; Multidimensional systems; Product codes;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/TIT.1972.1054914
Filename :
1054914
Link To Document :
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