Information on Result #946110
Linear OOA(2117, 692, F2, 3, 21) (dual of [(692, 3), 1959, 22]-NRT-code), using OOA 3-folding based on linear OA(2117, 2076, F2, 21) (dual of [2076, 1959, 22]-code), using
- discarding factors / shortening the dual code 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
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(2117, 692, F2, 3, 20) (dual of [(692, 3), 1959, 21]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2118, 692, F2, 3, 21) (dual of [(692, 3), 1958, 22]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2117, 692, F2, 4, 21) (dual of [(692, 4), 2651, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(2117, 692, F2, 5, 21) (dual of [(692, 5), 3343, 22]-NRT-code) | [i] | ||
| 5 | Linear OOA(2117, 692, F2, 6, 21) (dual of [(692, 6), 4035, 22]-NRT-code) | [i] | ||
| 6 | Linear OOA(2117, 692, F2, 7, 21) (dual of [(692, 7), 4727, 22]-NRT-code) | [i] | ||
| 7 | Linear OOA(2117, 692, F2, 8, 21) (dual of [(692, 8), 5419, 22]-NRT-code) | [i] | ||
| 8 | Digital (96, 117, 692)-net over F2 | [i] | ||