Universality of Pseudorandom series

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Pseudorandom series, such as Gold codes and Voyager coding, are explored for their potential application in universal communication systems. These codes can enhance signal quality by narrowing bandwidth and improving signal-to-noise ratios, despite the long transmission times associated with light-speed communication. The discussion raises questions about the necessity of using pseudorandom numbers if the receiver is unaware of the transmitted sequence, suggesting simpler alternatives might suffice. Additionally, the concept of long sequences for high-resolution measurements is highlighted, particularly in the context of SETI, which may struggle with synchronization over extended periods. Overall, the conversation emphasizes the complexities and potential benefits of using pseudorandom series in communication technologies.
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I was involved with pseudorandom series for communications.
For example Gold codes and Voyger randing codes. Do these codes apply with other number systems and hence throughout the universe.
Light speed communication will take years hence codes could be very long, giving very narrow bandwidth and good signal to noise, message may take years to say hello but nice to hear anyway.
Doug
 
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Why do you want to use pseudorandom numbers for communication, especially if the receiver does not know what you send? Why not just send the bits you want to transmit?

What is a "Voyger randing code"? Google gives this thread as top result.
 
This is spread spectrum ; because of correlation the longer the code sequence the narrower the bandwidth and better the signal to noise, I think a short gold code sequence is used for synchronization on your mobile phone. Think of 1024 bit sequence as 1 bit with error correction.
A long sequence was devised for Voyeur , long enough to think of it as a measure tape with no ambiguity over light hours hence high resolution..
SETI allows for spread spectrum (somewhat) but would not recognize long sequences without synchronization and patience of years?
 

Thread 'Deductive proof in logic formal systems'

I was reading documentation about the soundness and completeness of logic formal systems. Consider the following $$\vdash_S \phi$$ where ##S## is the proof-system making part the formal system and ##\phi## is a wff (well formed formula) of the formal language. Note the blank on left of the turnstile symbol ##\vdash_S##, as far as I can tell it actually represents the empty set. So what does it mean ? I guess it actually means ##\phi## is a theorem of the formal system, i.e. there is a...
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