Information on Result #808693
Linear OOA(2203, 530, F2, 2, 41) (dual of [(530, 2), 857, 42]-NRT-code), using OOA 2-folding based on linear OA(2203, 1060, F2, 41) (dual of [1060, 857, 42]-code), using
- construction XX applied to C1 = C([1019,34]), C2 = C([0,36]), C3 = C1 + C2 = C([0,34]), and C∩ = C1 ∩ C2 = C([1019,36]) [i] based on
- linear OA(2186, 1023, F2, 39) (dual of [1023, 837, 40]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,34}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(2176, 1023, F2, 37) (dual of [1023, 847, 38]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,36], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(2196, 1023, F2, 41) (dual of [1023, 827, 42]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,36}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(2166, 1023, F2, 35) (dual of [1023, 857, 36]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,34], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(26, 26, F2, 3) (dual of [26, 20, 4]-code or 26-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
- linear OA(21, 11, F2, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(2203, 530, F2, 3, 41) (dual of [(530, 3), 1387, 42]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2203, 530, F2, 4, 41) (dual of [(530, 4), 1917, 42]-NRT-code) | [i] | ||
| 3 | Linear OOA(2203, 530, F2, 5, 41) (dual of [(530, 5), 2447, 42]-NRT-code) | [i] | ||
| 4 | Linear OOA(2203, 530, F2, 6, 41) (dual of [(530, 6), 2977, 42]-NRT-code) | [i] | ||
| 5 | Linear OOA(2203, 530, F2, 7, 41) (dual of [(530, 7), 3507, 42]-NRT-code) | [i] | ||
| 6 | Linear OOA(2203, 530, F2, 8, 41) (dual of [(530, 8), 4037, 42]-NRT-code) | [i] | ||
| 7 | Digital (162, 203, 530)-net over F2 | [i] | ||