Abstract
Linear orthogonal binary sequences, special M-Sequences, are used widely in the systems communication channels as in the forward links for mixing the information on connection and as in the backward links of these channels to sift this information which transmitted and the receivers get the information in a correct form In current research trying study the construction of the linear equivalent of a product sequence on two, three, and four degrees over a linear sequences from the field Fp, where p is larger than two, and answering on the request, how is the maximum length of the linear equivalent of a product sequence (on a linear sequence {an} over the field Fp), is it less than rNh as the binary sequences?, or can reach it ?, or the length is exceed this value rNh? And is the product sequences are orthogonal? And we show that in some cases, the maximum length rNh for the binary sequences is not correct for the linear sequences in the finite field Fp for p larger than two and the result product sequences are not orthogonal, also trying study the product sequence on two different LFSRs, and how can use one shift feedback shift register LFSR as a monitor register of other p registers. In the current time, I think, there is no coders or decoders using the sequences over finite fields Fp where p is larger than 2 and from this idea this article showing very need for using in the future.
Highlights
The main obstacle to encoding and decoding is the complexity of decoding and decoding
In all stages of the encoding and the decoding, the orthogonal sequences play the main role in these processes, including the sequences with maximum period M-Sequences, Walsh sequences, Reed-Solomon sequences, and other sequences. [6,7,8,9,10,11,12]
2) If the sequence {zn} is multiplication on only two degrees of the recurring sequence {an} over Fp and the characteristic polynomial of the sequence {an} is prime of degree r the sequence {zn} is periodic and its period is equal to that is the half period of {an} but the set of the cyclic permutations of one period of {zn}is don’t form an orthogonal set as the sequence {an}
Summary
The main obstacle to encoding and decoding is the complexity of decoding and decoding. For this reason, efforts have been made to design cryptographic and decoding methods in an easy way. In all stages of the encoding and the decoding, the orthogonal sequences play the main role in these processes, including the sequences with maximum period M-Sequences, Walsh sequences, Reed-Solomon sequences, and other sequences. Shannon's classic articles, 1948-1949, were followed by many research papers on the question of finding successful ways to encode and successful decoding the media to allow it to be transmitted correctly through jammed channels. H., Studied the case for p=2. [15]
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