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[N. J. A. Sloane]

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.