Information on Result #2175096
Linear OA(2172, 561, F2, 37) (dual of [561, 389, 38]-code), using adding a parity check bit based on linear OA(2171, 560, F2, 36) (dual of [560, 389, 37]-code), using
- construction XX applied to C1 = C([477,0]), C2 = C([485,2]), C3 = C1 + C2 = C([485,0]), and C∩ = C1 ∩ C2 = C([477,2]) [i] based on
- linear OA(2145, 511, F2, 35) (dual of [511, 366, 36]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−34,−33,…,0}, and designed minimum distance d ≥ |I|+1 = 36 [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(2118, 511, F2, 27) (dual of [511, 393, 28]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−26,−25,…,0}, and designed minimum distance d ≥ |I|+1 = 28 [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, 10, F2, 1) (dual of [10, 9, 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(2174, 563, F2, 37) (dual of [563, 389, 38]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(2172, 280, F2, 2, 37) (dual of [(280, 2), 388, 38]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2172, 187, F2, 3, 37) (dual of [(187, 3), 389, 38]-NRT-code) | [i] | ||
| 4 | Linear OOA(2172, 140, F2, 4, 37) (dual of [(140, 4), 388, 38]-NRT-code) | [i] | ||