Tables of lower bounds for DNA codes with constant GC-content

Guide to superscripts: Multiple superscripts are occasionally given when codes have special structure (e.g. "l" and "c"), except when "p" applies.
Entries followed by periods are optimal by the Johnson-type upper bounds in [K].
Entries followed by are colons are optimal by max-clique computations in [CL].

References:

Please e-mail Philippe Gaborit (gaborit-at-unilim.fr) or Oliver King (ok-at-csua.berkeley.edu) with improvements or questions.

 

Lower bounds for A4GC(n,d,w):

n\d 34567891011121314151617181920
4 12.s,l 4.p ----------------
5 30:m 10.l 3.p - - - - -----------
6 112m 40.l 8:s,l 4.p - - - -----------
7 274m 72m 22l 7.l 3.p - - -----------
8 1056m 256d 56l,c 28v 5.l 4.p - -----------
9 3012m 555m 134a 40l 16m 5.l 3.p -----------
10 10622m 1710a 420c 116c 34v 16.l 5.l 4.p ----------
11 32636m 7392c 1848c 462c 73v 32l 11.v 4.l 3.p ---------
12 118272c 29568c 2994m 1848c 183v 68l 24v 9.m 4.p 4.p --------
13 473088c 109824c 8614m 1921m 440l 134m 46v 20l 8.m 4.l 3.p -------
14 1537536c 384384c 27456l 6076c 1534c 404c 112m 38l 16m 8.l 4.p 4.p ------
15 6589440c 1647360c 96096c 25740c 6470c 1575c 225m 107c 32v 14v 6.m 4.m 3.p -----
16 26357760c 6589440c 411840c 111360c 25880c 6680c 532m 177l 117c 60c 12.m 5.m 4.p 4.p ----
17 105431040c 26357760c 1555840c 390080c 48620c 24310c 1272l 380l 132l 123c 23v 9.m 5.m 4.m 3.p ---
18 210862080c 26357760c 5601024c 1400704c 87516c 87516c 3192l 920l 280v 123c 44v 19v 9.m 5.m 4.p 4.p --
19 756760576c 94595072c 22404096c 5922048c 370128c 92378c 7038m 2047v 615v 206v 81v 37v 15m 8.m 5.m 4.m 3.p -
20 3027042304c 378380288c 94595072c 23688192c 1478048c 369120c 23100c 5882c 1461c 457v 166v 67v 31c 13m 8.m 5.m 4.p 4.p
(examples of linear codes from which entries were derived)

 

Lower bounds for A4GC,RC(n,d,w):

n\d34567891011121314151617181920
4 6.s,l 2.p - - - - - -----------
5 15:l 3:l 1.p - - - - -----------
6 44a 16:l 4.l 2.p - - - -----------
7 135a 36b 11:m 2:l 1.p - - -----------
8 528m 128d 28b 12s 2.p 2.p - -----------
9 1354m 275a 67a 20a 8m 2.l 1.p -----------
10 4542m 855a 175a 54c 16a 8.l 2.p 2.p ----------
11 14405m 2457m 477a 117a 37v 14v 5.m 2.m 1.p ---------
12 58976c 14624c 1381v 924c 87v 29v 11m 4.s,l 2.p 2.p --------
13 167263m 27376c 3974v 924c 206v 62v 22a 9m 4.m 2.m 1.p -------
14 430080c 192192c 11878c 2963c 749c 180c 48v 19v 8v 4.m 2.p 2.p ------
15 1646240c 411821c 25670c 6634v 1600c 347v 106v 37v 18m 6m 3.m 2.m 1.p -----
16 13174400c 3293600c 55376c 55376c 12864c 3264c 238v 78v 52c 24c 5m 2.p 2.p 2.p ----
17 26355520c 6587200c 97450c 97450c 12864c 6060c 579v 172v 60v 30c 11m 4.m 2.m 2.m 1.p ---
18 44808192c 11202048c 698592c 698592c 41784c 10496c 1459l 407l 129m 47m 20m 9m 4.m 2.p 2.p 2.p --
19 47102080c 23647760c 698592c 698592c 46838m 11319c 3519m 960v 285v 96v 37v 16m 7m 4.m 2.m 2.m 1.p -
20 756760576c 189189536c 11806240c 11806240c 184756c 184756c 11452c 2868c 766c 179c 76v 31v 14m 6m 4.m 2.p 2.p 2.p
(examples of linear codes from which entries were derived)

 

Last updated February 25, 2008
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