Information on Result #2478802
Linear OOA(2119, 1039, F2, 2, 20) (dual of [(1039, 2), 1959, 21]-NRT-code), using 21 times duplication based on linear OOA(2118, 1039, F2, 2, 20) (dual of [(1039, 2), 1960, 21]-NRT-code), using
- strength reduction [i] based on linear OOA(2118, 1039, F2, 2, 21) (dual of [(1039, 2), 1960, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2118, 2078, F2, 21) (dual of [2078, 1960, 22]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2117, 2077, F2, 21) (dual of [2077, 1960, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- linear OA(2111, 2049, F2, 21) (dual of [2049, 1938, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- 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(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([0,10]) ⊂ C([0,8]) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(2117, 2077, F2, 21) (dual of [2077, 1960, 22]-code), using
- OOA 2-folding [i] based on linear OA(2118, 2078, F2, 21) (dual of [2078, 1960, 22]-code), using
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(2119, 823, F2, 3, 20) (dual of [(823, 3), 2350, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2119, 823, F2, 4, 20) (dual of [(823, 4), 3173, 21]-NRT-code) | [i] | ||
| 3 | Linear OOA(2119, 823, F2, 5, 20) (dual of [(823, 5), 3996, 21]-NRT-code) | [i] | ||
| 4 | Linear OOA(2119, 823, F2, 6, 20) (dual of [(823, 6), 4819, 21]-NRT-code) | [i] | ||
| 5 | Linear OOA(2119, 823, F2, 7, 20) (dual of [(823, 7), 5642, 21]-NRT-code) | [i] | ||
| 6 | Linear OOA(2119, 823, F2, 8, 20) (dual of [(823, 8), 6465, 21]-NRT-code) | [i] | ||
| 7 | Digital (99, 119, 823)-net over F2 | [i] | ||