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 288v 78v 22l 7.l 3.p - - -----------
8 1056m 256d 63v 28v 5.l 4.p - -----------
9 3012m 555m 134a 48v 18v 5.l 3.p -----------
10 10622m 2016v 420c 116c 34v 16.l 5.l 4.p ----------
11 32636m 7392c 1848c 462c 75v 32l 11.v 4.l 3.p ---------
12 118272c 29568c 2994m 1848c 183v 118v 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 40v 17v 8.l 4.p 4.p ------
15 6589440c 1647360c 96096c 25740c 6960v 1575c 227v 107c 34v 15v 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 24v 9.m 5.m 4.m 3.p ---
18 210862080c 26357760c 5601024c 1400704c 87516c 87516c 3192l 920l 282v 123c 46v 20v 9.m 5.m 4.p 4.p --
19 756760576c 94595072c 22404096c 5922048c 370128c 92378c 7038m 2047v 615v 213v 83v 38v 17m 8.m 5.m 4.m 3.p -
20 3027042304c 378380288c 94595072c 23688192c 1478048c 369120c 23100c 5882c 1461c 457v 167v 69v 33v 16v 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 21v 8m 2.l 1.p -----------
10 4542m 855a 176v 54c 17v 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 12v 4.s,l 2.p 2.p --------
13 167263m 27376c 3974v 924c 206v 62v 23v 10v 4.m 2.m 1.p -------
14 430080c 192192c 11878c 2963c 749c 180c 49v 20v 8v 4.m 2.p 2.p ------
15 1646240c 411821c 25670c 6634v 1600c 347v 109v 37v 18m 6m 3.m 2.m 1.p -----
16 13174400c 3293600c 55376c 55376c 12864c 3264c 243v 83v 52c 24c 5m 2.p 2.p 2.p ----
17 26355520c 6587200c 97450c 97450c 12864c 6060c 579v 175v 62v 30c 12v 4.m 2.m 2.m 1.p ---
18 44808192c 11202048c 698592c 698592c 41784c 10496c 1459l 407l 133v 49v 21v 10v 4.m 2.p 2.p 2.p --
19 47102080c 23647760c 698592c 698592c 46838m 11319c 3678v 960v 285v 99v 39v 18v 8v 4.m 2.m 2.m 1.p -
20 756760576c 189189536c 11806240c 11806240c 184756c 184756c 11452c 2868c 766c 179c 77v 33v 15v 7v 4.m 2.p 2.p 2.p
(examples of linear codes from which entries were derived)

 

Last updated August 18, 2009
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