Information on Result #701866
Linear OA(2142, 299, F2, 34) (dual of [299, 157, 35]-code), using construction XX applied to C1 = C([239,16]), C2 = C([237,8]), C3 = C1 + C2 = C([239,8]), and C∩ = C1 ∩ C2 = C([237,16]) based on
- linear OA(2121, 255, F2, 33) (dual of [255, 134, 34]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−16,−15,…,16}, and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(2101, 255, F2, 27) (dual of [255, 154, 28]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−18,−17,…,8}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(2125, 255, F2, 35) (dual of [255, 130, 36]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−18,−17,…,16}, and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(297, 255, F2, 25) (dual of [255, 158, 26]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−16,−15,…,8}, and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(216, 39, F2, 6) (dual of [39, 23, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(216, 42, F2, 6) (dual of [42, 26, 7]-code), using
- extracting embedded orthogonal array [i] based on digital (10, 16, 42)-net over F2, using
- discarding factors / shortening the dual code based on linear OA(216, 42, F2, 6) (dual of [42, 26, 7]-code), using
- linear OA(21, 5, F2, 1) (dual of [5, 4, 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(2143, 300, F2, 35) (dual of [300, 157, 36]-code) | [i] | Adding a Parity Check Bit | |
| 2 | Linear OOA(2142, 149, F2, 2, 34) (dual of [(149, 2), 156, 35]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2142, 99, F2, 3, 34) (dual of [(99, 3), 155, 35]-NRT-code) | [i] | ||