Information on Result #703044
Linear OA(2238, 1046, F2, 48) (dual of [1046, 808, 49]-code), using construction XX applied to C1 = C([1021,44]), C2 = C([1,46]), C3 = C1 + C2 = C([1,44]), and C∩ = C1 ∩ C2 = C([1021,46]) based on
- linear OA(2226, 1023, F2, 47) (dual of [1023, 797, 48]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,44}, and designed minimum distance d ≥ |I|+1 = 48 [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(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(2215, 1023, F2, 44) (dual of [1023, 808, 45]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(21, 12, F2, 1) (dual of [12, 11, 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
- 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 (see above)
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(2239, 1047, F2, 49) (dual of [1047, 808, 50]-code) | [i] | Adding a Parity Check Bit | |
| 2 | Linear OOA(2238, 523, F2, 2, 48) (dual of [(523, 2), 808, 49]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2238, 209, F2, 5, 48) (dual of [(209, 5), 807, 49]-NRT-code) | [i] | ||