Maximal Length LFSR Feedback Terms

This directory holds data files with maximal length LFSR feedback polynomials. LFSRs have uses as pseudo-random number generators in several application domains. It is not my intent to teach or support LFSR design -- just to make available some feedback terms I computed.

If you want to know more about LFSR usage, some starting points are:

RSA Laboratories: what is a stream cipher?
Linear Complexity: A Literature Survey
A more sophisticated program to do this was at ftp://helsbreth.org/pub/helsbret/random/lfsr_s.c (the author says that his results agree with the tables below, but that code is no longer available). A newer program is here: https://bitbucket.org/gallen/mlpolygen/overview

For more on primitive polynomials, see:

The following table is probably may be updated from time to time as my workstations have spare cycles to do more computations. You may use these results as you like, but since this is free I give no warrantee on them for any purpose whatsoever. If you find a problem, please let me know and I will fix it if/when I have time.

SIZE (# bits in feedback term)	# Feedback terms found	Text file (First hundred entries)	Gzip'ed file (complete list)
4	2	4.txt	4.dat.gz
5	6	5.txt	5.dat.gz
6	6	6.txt	6.dat.gz
7	18	7.txt	7.dat.gz
8	16	8.txt	8.dat.gz
9	48	9.txt	9.dat.gz
10	60	10.txt	10.dat.gz
11	176	11.txt	11.dat.gz
12	144	12.txt	12.dat.gz
13	630	13.txt	13.dat.gz
14	756	14.txt	14.dat.gz
15	1,800	15.txt	15.dat.gz
16	2,048	16.txt	16.dat.gz
17	7,710	17.txt	17.dat.gz
18	7,776	18.txt	18.dat.gz
19	27,594	19.txt	19.dat.gz
20	24,000	20.txt	20.dat.gz
21	84,672	21.txt	21.dat.gz
22	120,032	22.txt	22.dat.gz
23	356,960	23.txt	23.dat.gz
24	276,480	24.txt	24.dat.gz
25	1,296,000	25.txt	25.dat.gz
26	1,719,900	26.txt	26.dat.gz
27	4,202,496	27.txt	27.dat.gz
28	4,741,632	28.txt	28.dat.gz
29	18,407,808	29.txt	29.dat.gz
30	17,820,000	30.txt	30.dat.gz
31	69,273,666	31.txt	31.dat.gz (184 MB!)
32	67,108,864	32.txt	32.dat.gz (186 MB!)
33	--	33.txt
34	--	34.txt
35	--	35.txt
36	--	36.txt
37	--	37.txt
38	--	38.txt
39	--	39.txt
40	--	40.txt
41	--	41.txt
42	--	42.txt
43	--	43.txt
44	--	44.txt
45	--	45.txt
46	--	46.txt
47	--	47.txt
48	--	48.txt
49	--	49.txt
50	--	50.txt
51	--	51.txt
52	--	52.txt
53	--	53.txt
54	--	54.txt
55	--	55.txt
56	--	56.txt
57	--	57.txt
58	--	58.txt
59	--	59.txt
60	--	60.txt
61	--	61.txt
62	--	62.txt
63	--	63.txt
64	--	64.txt

In the above data files, the feedback term is the hexadecimal number that represents the feedback polynomial for a right-shifted LFSR per the following C code LFSR inner loop implementation:

  if (i & 1)  { i = (i >> 1) ^ feed; }
  else        { i = (i >> 1);       }

Philip Koopman