Information on Result #1097208
Linear OOA(2252, 6562, F2, 5, 33) (dual of [(6562, 5), 32558, 34]-NRT-code), using OOA 5-folding based on linear OA(2252, 32810, F2, 33) (dual of [32810, 32558, 34]-code), using
- 4 times code embedding in larger space [i] based on linear OA(2248, 32806, F2, 33) (dual of [32806, 32558, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,14]) [i] based on
- linear OA(2241, 32769, F2, 33) (dual of [32769, 32528, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 230−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(2211, 32769, F2, 29) (dual of [32769, 32558, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 230−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(27, 37, F2, 3) (dual of [37, 30, 4]-code or 37-cap in PG(6,2)), using
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 4 [i]
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- construction X applied to C([0,16]) ⊂ C([0,14]) [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(2251, 6561, F2, 5, 32) (dual of [(6561, 5), 32554, 33]-NRT-code) | [i] | Truncation for OOAs | |
| 2 | Linear OOA(2252, 6159, F2, 6, 33) (dual of [(6159, 6), 36702, 34]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(2252, 6159, F2, 7, 33) (dual of [(6159, 7), 42861, 34]-NRT-code) | [i] | ||
| 4 | Linear OOA(2252, 6159, F2, 8, 33) (dual of [(6159, 8), 49020, 34]-NRT-code) | [i] | ||
| 5 | Digital (219, 252, 6159)-net over F2 | [i] | ||