Information on Result #945686
Linear OOA(295, 692, F2, 3, 17) (dual of [(692, 3), 1981, 18]-NRT-code), using OOA 3-folding based on linear OA(295, 2076, F2, 17) (dual of [2076, 1981, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(295, 2077, F2, 17) (dual of [2077, 1982, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,6]) [i] based on
- linear OA(289, 2049, F2, 17) (dual of [2049, 1960, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(267, 2049, F2, 13) (dual of [2049, 1982, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(26, 28, F2, 3) (dual of [28, 22, 4]-code or 28-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to C([0,8]) ⊂ C([0,6]) [i] based on
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
Result | This result only | Method | ||
---|---|---|---|---|
1 | Linear OOA(295, 692, F2, 3, 16) (dual of [(692, 3), 1981, 17]-NRT-code) | [i] | Strength Reduction for OOAs | |
2 | Linear OOA(296, 692, F2, 3, 17) (dual of [(692, 3), 1980, 18]-NRT-code) | [i] | OOA Duplication | |
3 | Linear OOA(295, 692, F2, 4, 17) (dual of [(692, 4), 2673, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
4 | Linear OOA(295, 692, F2, 5, 17) (dual of [(692, 5), 3365, 18]-NRT-code) | [i] | ||
5 | Linear OOA(295, 692, F2, 6, 17) (dual of [(692, 6), 4057, 18]-NRT-code) | [i] | ||
6 | Linear OOA(295, 692, F2, 7, 17) (dual of [(692, 7), 4749, 18]-NRT-code) | [i] | ||
7 | Linear OOA(295, 692, F2, 8, 17) (dual of [(692, 8), 5441, 18]-NRT-code) | [i] | ||
8 | Digital (78, 95, 692)-net over F2 | [i] |