Information on Result #702523
Linear OA(2220, 560, F2, 48) (dual of [560, 340, 49]-code), using construction XX applied to C1 = C([507,40]), C2 = C([1,44]), C3 = C1 + C2 = C([1,40]), and C∩ = C1 ∩ C2 = C([507,44]) based on
- 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 = {−4,−3,…,40}, and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(2189, 511, F2, 44) (dual of [511, 322, 45]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(2208, 511, F2, 49) (dual of [511, 303, 50]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−4,−3,…,44}, and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(2171, 511, F2, 40) (dual of [511, 340, 41]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [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(26, 24, F2, 3) (dual of [24, 18, 4]-code or 24-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)) (see above)
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(2222, 562, F2, 48) (dual of [562, 340, 49]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(2221, 561, F2, 49) (dual of [561, 340, 50]-code) | [i] | Adding a Parity Check Bit | |
| 3 | Linear OA(2229, 579, F2, 48) (dual of [579, 350, 49]-code) | [i] | Varšamov–Edel Lengthening | |
| 4 | Linear OA(2230, 583, F2, 48) (dual of [583, 353, 49]-code) | [i] | ||
| 5 | Linear OA(2231, 588, F2, 48) (dual of [588, 357, 49]-code) | [i] | ||
| 6 | Linear OA(2223, 564, F2, 48) (dual of [564, 341, 49]-code) | [i] | Construction X with Varšamov Bound | |
| 7 | Linear OOA(2220, 280, F2, 2, 48) (dual of [(280, 2), 340, 49]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(2220, 140, F2, 4, 48) (dual of [(140, 4), 340, 49]-NRT-code) | [i] | ||