10 August 2018

LINK-11 CLEW, doubts about the generator polynomial x^5+x+1

I have some doubts about the description at page 19 of MIL 188-203-1A (Tadil-A/Link-11) [1]: the document states that the Start Code and the Address Code frames " [...] are equivalent to 60-bit portions of the maximum-length shift register sequence with generator polynomial G(x) =  x5+x+1" ...but such a fifth grade polinomyal has a maximum length sequence (MLS) of 31 bits (25-1). Indeed, I found the generator polymonial x6+x+1, whose MLS is 63, for both start and address frames:

Using a GNU Octave script [2] I also checked the three fundamental properties of LFSR maximum length sequences: Balance Property, Runlength Property, and Autocorrelation Property [3]: verification fails for x5+x+1

  • The Code does NOT satisfy Balance Property: number of 1s and 0s are 17 14
  • The code does NOT satisfy RUN LENGTH property: the run length is 10    2    1    1    2
  • The Code does NOT satisfy the Autocorrelation Property

  while verification is ok for x6+x+1 
  • The Code satisfies Balance Property: number of 1s and 0s are 32 31
  • The code satisfies RUN LENGTH property: the run length is 16    8    4    2    1    1
  • The Code satisfies the Autocorrelation Property

So I do not know if I'm wrong or if there's a typo in 188-203-1A, comments are welcome.