Information on Result #1096864
Linear OOA(2222, 6562, F2, 5, 29) (dual of [(6562, 5), 32588, 30]-NRT-code), using OOA 5-folding based on linear OA(2222, 32810, F2, 29) (dual of [32810, 32588, 30]-code), using
- 4 times code embedding in larger space [i] based on linear OA(2218, 32806, F2, 29) (dual of [32806, 32588, 30]-code), using
- construction X applied to C([0,14]) ⊂ C([0,12]) [i] based on
- 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(2181, 32769, F2, 25) (dual of [32769, 32588, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 230−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (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([0,14]) ⊂ C([0,12]) [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(2221, 6561, F2, 5, 28) (dual of [(6561, 5), 32584, 29]-NRT-code) | [i] | Truncation for OOAs | |
| 2 | Linear OOA(2222, 6492, F2, 6, 29) (dual of [(6492, 6), 38730, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(2222, 6492, F2, 7, 29) (dual of [(6492, 7), 45222, 30]-NRT-code) | [i] | ||
| 4 | Linear OOA(2222, 6492, F2, 8, 29) (dual of [(6492, 8), 51714, 30]-NRT-code) | [i] | ||
| 5 | Digital (193, 222, 6492)-net over F2 | [i] | ||