Information on Result #703050
Linear OA(2253, 1060, F2, 51) (dual of [1060, 807, 52]-code), using construction XX applied to C1 = C([1019,44]), C2 = C([0,46]), C3 = C1 + C2 = C([0,44]), and C∩ = C1 ∩ C2 = C([1019,46]) based on
- linear OA(2236, 1023, F2, 49) (dual of [1023, 787, 50]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,44}, and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(2226, 1023, F2, 47) (dual of [1023, 797, 48]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,46], and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(2246, 1023, F2, 51) (dual of [1023, 777, 52]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,46}, and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(2216, 1023, F2, 45) (dual of [1023, 807, 46]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,44], and designed minimum distance d ≥ |I|+1 = 46 [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 OA(2252, 1059, F2, 50) (dual of [1059, 807, 51]-code) | [i] | Truncation | |
| 2 | Linear OOA(2253, 530, F2, 2, 51) (dual of [(530, 2), 807, 52]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2253, 353, F2, 3, 51) (dual of [(353, 3), 806, 52]-NRT-code) | [i] | ||
| 4 | Linear OOA(2253, 265, F2, 4, 51) (dual of [(265, 4), 807, 52]-NRT-code) | [i] | ||
| 5 | Linear OOA(2253, 212, F2, 5, 51) (dual of [(212, 5), 807, 52]-NRT-code) | [i] | ||
| 6 | Linear OOA(2253, 176, F2, 6, 51) (dual of [(176, 6), 803, 52]-NRT-code) | [i] | ||
| 7 | Linear OOA(2253, 151, F2, 7, 51) (dual of [(151, 7), 804, 52]-NRT-code) | [i] | ||