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N. J. A. Sloane
njas at research.att.com
Sat Mar 21 20:03:36 CET 1998
Dear friends: "Constant weight codes":
Let A(n,d,w) denote the max possible number of binary
vectors of length n, each containing exactly w 1's
and n-w 0's, and such that the Hamming distance
between any 2 vectors is at least d.
[BSSS90] (see below) give tables of lower bounds for n <= 28.
(These table will soon be on my home page, www.research.att.com/~njas)
For a new application I need further lower bounds (i.e. constructions),
especially for A(n,8,8). Here is what I have at present,
but many of these entries below 28 are VERY weak.
Any improvements should be sent to njas at research.att.com !
Thanks, Neil Sloane
A(n,8,8)
n >= from
10 1. [BSSS90]
11 1. [BSSS90]
12 3. [BSSS90]
13 3. [BSSS90]
14 7. [BSSS90]
15 15. [BSSS90]
16 30. [BSSS90]
17 34. S(5,8,24)
18 46. S(5,8,24)
19 78. S(5,8,24)
20 130. S(5,8,24)
21 210. S(5,8,24)
22 330. S(5,8,24)
23 506. S(5,8,24)
24 759. S(5,8,24)
25 759 [BSSS90]
26 760 [BSSS90]
27 766 [BSSS90]
28 833 [BSSS90]
29 833
30 833
31 913 Lex
32 1068 Lex
33 1068
34 1068
35 1148 Sh
36 1344 Sh
37 1636 Sh
38 2036 Sh
39 2036
40 2036
41 2133 RR
42 2537 RR
43 3073 RR
44 3751 RR
45 4423 RR
46 5243 RR
47 6275 RR
48 7530 RR
KEY
. A dot means entry is exact.
[BSSS90]: A. E. Brouwer et al., A new table of
constant weight codes, IEEE Trans. Infor, Theory,
36 (1990), 1334--1380. (Not yet on my home page.)
Lex: Lexicode.
RR: From Rao-Reddy [48,21,8] code
by puncturing first k coords from the set
{1,2,3,4,21,22,23,24,41,42,43,44}
referring to my standard version.
Sh: From Shearer's [38,22,8] code
by puncturing coordinates from the end.
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