Information on Result #702317
Linear OA(2174, 564, F2, 36) (dual of [564, 390, 37]-code), using construction XX applied to C1 = C([477,510]), C2 = C([485,2]), C3 = C1 + C2 = C([485,510]), and C∩ = C1 ∩ C2 = C([477,2]) based on
- linear OA(2144, 511, F2, 34) (dual of [511, 367, 35]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−34,−33,…,−1}, and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(2127, 511, F2, 29) (dual of [511, 384, 30]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−26,−25,…,2}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(2154, 511, F2, 37) (dual of [511, 357, 38]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−34,−33,…,2}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(2117, 511, F2, 26) (dual of [511, 394, 27]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−26,−25,…,−1}, and designed minimum distance d ≥ |I|+1 = 27 [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(24, 14, F2, 2) (dual of [14, 10, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(24, 15, F2, 2) (dual of [15, 11, 3]-code), using
- Hamming code H(4,2) [i]
- discarding factors / shortening the dual code based on linear OA(24, 15, F2, 2) (dual of [15, 11, 3]-code), 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(2175, 565, F2, 37) (dual of [565, 390, 38]-code) | [i] | Adding a Parity Check Bit | |
| 2 | Linear OOA(2174, 282, F2, 2, 36) (dual of [(282, 2), 390, 37]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2174, 188, F2, 3, 36) (dual of [(188, 3), 390, 37]-NRT-code) | [i] | ||
| 4 | Linear OOA(2174, 141, F2, 4, 36) (dual of [(141, 4), 390, 37]-NRT-code) | [i] | ||