Size of a CRC (or similar) code for a given length of message

From	James Harris <james.harris.1@gmail.com>
Newsgroups	comp.programming
Subject	Size of a CRC (or similar) code for a given length of message
Date	2015-09-25 10:59 +0100
Organization	A noiseless patient Spider
Message-ID	<mu35qo$o6g$1@dont-email.me> (permalink)

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I see from

   https://en.wikipedia.org/wiki/Cyclic_redundancy_check

that, typically, an n-bit CRC applied to a data block of arbitrary 
length will detect a single error burst up to n bits long.

That's fine - or as fine as the complex mathematics of CRCs gets! - but 
if looking to select a CRC calculation (or some other data integrity 
check) are there any guidelines on how wide the CRC code should be for 
given levels of assurance against random corruption for a given size of 
message?

At the moment I am looking to protect a very short header of about 12 
bytes, give or take, and wonder what levels of confidence a certain 
number of CRC bits would give against data corruption.

For example, if I used a 3-bit CRC to protect a 12-byte header how 
'good' would that be compared to a 5-bit CRC? And if the header became 
24 bytes, say, what effect would that have on the effectiveness of 3-bit 
and 5-bit CRCs? (Always assuming that other aspects of the CRC 
calculation are chosen well.)

If I later wanted to protect a message of a thousand or a 
hundred-thousand bytes how wide would the CRC need to be to maintain a 
similar level of confidence?

Any ideas?

James

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Size of a CRC (or similar) code for a given length of message James Harris <james.harris.1@gmail.com> - 2015-09-25 10:59 +0100
  Re: Size of a CRC (or similar) code for a given length of message David Brown <david.brown@hesbynett.no> - 2015-09-25 13:05 +0200
    Re: Size of a CRC (or similar) code for a given length of message James Harris <james.harris.1@gmail.com> - 2015-09-25 13:42 +0100
      Re: Size of a CRC (or similar) code for a given length of message David Brown <david.brown@hesbynett.no> - 2015-09-25 15:15 +0200
  Re: Size of a CRC (or similar) code for a given length of message Julio Di Egidio <julio@diegidio.name> - 2015-09-25 04:07 -0700
    Re: Size of a CRC (or similar) code for a given length of message David Brown <david.brown@hesbynett.no> - 2015-09-25 14:32 +0200
      Re: Size of a CRC (or similar) code for a given length of message Julio Di Egidio <julio@diegidio.name> - 2015-09-25 05:40 -0700
    Re: Size of a CRC (or similar) code for a given length of message James Harris <james.harris.1@gmail.com> - 2015-09-25 13:45 +0100
  Re: Size of a CRC (or similar) code for a given length of message Öö Tiib <ootiib@hot.ee> - 2015-09-25 04:17 -0700
    Re: Size of a CRC (or similar) code for a given length of message David Brown <david.brown@hesbynett.no> - 2015-09-25 14:36 +0200
      Re: Size of a CRC (or similar) code for a given length of message James Harris <james.harris.1@gmail.com> - 2015-09-25 13:49 +0100

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