Information on Result #1663399
Linear OOA(2119, 693, F2, 6, 21) (dual of [(693, 6), 4039, 22]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2119, 693, F2, 3, 21) (dual of [(693, 3), 1960, 22]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2119, 2079, F2, 21) (dual of [2079, 1960, 22]-code), using
- 2 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
- 2 times code embedding in larger space [i] based on linear OA(2117, 2077, F2, 21) (dual of [2077, 1960, 22]-code), using
Mode: 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(2120, 693, F2, 6, 21) (dual of [(693, 6), 4038, 22]-NRT-code) | [i] | OOA Duplication | |