Information on Result #702638
Linear OA(2242, 546, F2, 56) (dual of [546, 304, 57]-code), using construction XX applied to C1 = C([507,50]), C2 = C([1,52]), C3 = C1 + C2 = C([1,50]), and C∩ = C1 ∩ C2 = C([507,52]) based on
- linear OA(2226, 511, F2, 55) (dual of [511, 285, 56]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−4,−3,…,50}, and designed minimum distance d ≥ |I|+1 = 56 [i]
- linear OA(2216, 511, F2, 52) (dual of [511, 295, 53]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,52], and designed minimum distance d ≥ |I|+1 = 53 [i]
- linear OA(2235, 511, F2, 57) (dual of [511, 276, 58]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−4,−3,…,52}, and designed minimum distance d ≥ |I|+1 = 58 [i]
- linear OA(2207, 511, F2, 50) (dual of [511, 304, 51]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,50], and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(26, 25, F2, 3) (dual of [25, 19, 4]-code or 25-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), 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(2244, 548, F2, 56) (dual of [548, 304, 57]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(2249, 553, F2, 56) (dual of [553, 304, 57]-code) | [i] | ||
| 3 | Linear OA(2243, 547, F2, 57) (dual of [547, 304, 58]-code) | [i] | Adding a Parity Check Bit | |
| 4 | Linear OA(2257, 580, F2, 56) (dual of [580, 323, 57]-code) | [i] | Varšamov–Edel Lengthening | |
| 5 | Linear OA(2258, 585, F2, 56) (dual of [585, 327, 57]-code) | [i] | ||
| 6 | Linear OA(2246, 551, F2, 56) (dual of [551, 305, 57]-code) | [i] | Construction X with Varšamov Bound | |
| 7 | Linear OA(2250, 558, F2, 56) (dual of [558, 308, 57]-code) | [i] | ||
| 8 | Linear OOA(2242, 273, F2, 2, 56) (dual of [(273, 2), 304, 57]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(2242, 182, F2, 3, 56) (dual of [(182, 3), 304, 57]-NRT-code) | [i] | ||
| 10 | Linear OOA(2242, 109, F2, 5, 56) (dual of [(109, 5), 303, 57]-NRT-code) | [i] | ||