Information on Result #703051
Linear OA(2251, 1049, F2, 51) (dual of [1049, 798, 52]-code), using construction XX applied to C1 = C([1021,46]), C2 = C([1,48]), C3 = C1 + C2 = C([1,46]), and C∩ = C1 ∩ C2 = C([1021,48]) 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 = {−2,−1,…,46}, and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(2235, 1023, F2, 48) (dual of [1023, 788, 49]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,48], and designed minimum distance d ≥ |I|+1 = 49 [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 = {−2,−1,…,48}, and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(2225, 1023, F2, 46) (dual of [1023, 798, 47]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,46], and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(24, 15, F2, 2) (dual of [15, 11, 3]-code), using
- Hamming code H(4,2) [i]
- 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(2251, 1049, F2, 50) (dual of [1049, 798, 51]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2250, 1048, F2, 50) (dual of [1048, 798, 51]-code) | [i] | Truncation | |