Information on Result #702539
Linear OA(2234, 560, F2, 52) (dual of [560, 326, 53]-code), using construction XX applied to C1 = C([461,0]), C2 = C([469,2]), C3 = C1 + C2 = C([469,0]), and C∩ = C1 ∩ C2 = C([461,2]) based on
- linear OA(2208, 511, F2, 51) (dual of [511, 303, 52]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−50,−49,…,0}, and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(2190, 511, F2, 45) (dual of [511, 321, 46]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−42,−41,…,2}, and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(2217, 511, F2, 53) (dual of [511, 294, 54]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−50,−49,…,2}, and designed minimum distance d ≥ |I|+1 = 54 [i]
- linear OA(2181, 511, F2, 43) (dual of [511, 330, 44]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−42,−41,…,0}, and designed minimum distance d ≥ |I|+1 = 44 [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(2235, 561, F2, 53) (dual of [561, 326, 54]-code) | [i] | Adding a Parity Check Bit | |
| 2 | Linear OA(2238, 566, F2, 52) (dual of [566, 328, 53]-code) | [i] | Varšamov–Edel Lengthening | |
| 3 | Linear OA(2239, 568, F2, 52) (dual of [568, 329, 53]-code) | [i] | ||
| 4 | Linear OA(2240, 570, F2, 52) (dual of [570, 330, 53]-code) | [i] | ||
| 5 | Linear OA(2239, 567, F2, 52) (dual of [567, 328, 53]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OA(2240, 569, F2, 52) (dual of [569, 329, 53]-code) | [i] | ||
| 7 | Linear OOA(2234, 280, F2, 2, 52) (dual of [(280, 2), 326, 53]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(2234, 186, F2, 3, 52) (dual of [(186, 3), 324, 53]-NRT-code) | [i] | ||
| 9 | Linear OOA(2234, 140, F2, 4, 52) (dual of [(140, 4), 326, 53]-NRT-code) | [i] | ||