see also
http://en.wikipedia.org/wiki/Computation_of_CRC

esp. parallel computation (tables)

3 bit crc is not much good, very short.  10 or 11 is really a
minimum :-)

have you a choice or is it communication with an existing system/
standard?

Cyclic Redundancy Codes (CRCs) provide a first line of defense against
data corruption in many networks. Unfortunately, many commonly used
CRC polynomials provide significantly less error detection capability
than they might. An exhaustive exploration reveals that most
previously published CRC polynomials are either inferior to
alternatives or are only good choices for particular message lengths.
Unfortunately these shortcomings and limitations often seem to be
overlooked. This paper describes a polynomial selection process for
embedded network applications and proposes a set of good general-
purpose polynomials. A set of 35 new polynomials in addition to 13
previously published polynomials provides good performance for 3- to
16-bit CRCs for data word lengths up to 2048 bits.

see http://www.ece.cmu.edu/~koopman/crc/index.html

also http://www.computing.dcu.ie/~humphrys/Notes/Networks/data.polynomial.html

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