Uniqueness of codes using semidefinite programming
For n , d , w ∈ N , let A ( n , d , w ) denote the maximum size of a binary code of word length n , minimum distance d and constant weight w . Schrijver recently showed using semidefinite programming that A ( 23 , 8 , 11 ) = 1288 , and the second author that A ( 22 , 8 , 11 ) = 672 and A (...
Uložené v:
| Vydané v: | Designs, codes, and cryptography Ročník 87; číslo 8; s. 1881 - 1895 |
|---|---|
| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
New York
Springer US
2019
Springer Nature B.V |
| Predmet: | |
| ISSN: | 0925-1022, 1573-7586, 1573-7586 |
| On-line prístup: | Získať plný text |
| Tagy: |
Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
|
| Shrnutí: | For
n
,
d
,
w
∈
N
, let
A
(
n
,
d
,
w
) denote the maximum size of a binary code of word length
n
, minimum distance
d
and constant weight
w
. Schrijver recently showed using semidefinite programming that
A
(
23
,
8
,
11
)
=
1288
, and the second author that
A
(
22
,
8
,
11
)
=
672
and
A
(
22
,
8
,
10
)
=
616
. Here we show uniqueness of the codes achieving these bounds. Let
A
(
n
,
d
) denote the maximum size of a binary code of word length
n
and minimum distance
d
. Gijswijt et al. showed that
A
(
20
,
8
)
=
256
. We show that there are several nonisomorphic codes achieving this bound, and classify all such codes with all distances divisible by 4. |
|---|---|
| Bibliografia: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23 Communicated by J. H. Koolen. |
| ISSN: | 0925-1022 1573-7586 1573-7586 |
| DOI: | 10.1007/s10623-018-0589-8 |