Information on Result #1151741
Linear OOA(2239, 299600, F2, 7, 23) (dual of [(299600, 7), 2096961, 24]-NRT-code), using OOA 7-folding based on linear OA(2239, 2097200, F2, 23) (dual of [2097200, 2096961, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2239, 2097201, F2, 23) (dual of [2097201, 2096962, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- linear OA(2232, 2097152, F2, 23) (dual of [2097152, 2096920, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2190, 2097152, F2, 19) (dual of [2097152, 2096962, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(27, 49, F2, 3) (dual of [49, 42, 4]-code or 49-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 Ce(22) ⊂ Ce(18) [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(2239, 299600, F2, 7, 22) (dual of [(299600, 7), 2096961, 23]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2240, 299600, F2, 7, 23) (dual of [(299600, 7), 2096960, 24]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2241, 299600, F2, 7, 23) (dual of [(299600, 7), 2096959, 24]-NRT-code) | [i] | ||
| 4 | Linear OOA(2242, 299600, F2, 7, 23) (dual of [(299600, 7), 2096958, 24]-NRT-code) | [i] | ||
| 5 | Linear OOA(2239, 290847, F2, 8, 23) (dual of [(290847, 8), 2326537, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Digital (216, 239, 290847)-net over F2 | [i] | ||