Information on Result #702039
Linear OA(2221, 268, F2, 88) (dual of [268, 47, 89]-code), using construction XX applied to C1 = C([251,84]), C2 = C([1,86]), C3 = C1 + C2 = C([1,84]), and C∩ = C1 ∩ C2 = C([251,86]) based on
- linear OA(2217, 255, F2, 89) (dual of [255, 38, 90]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−4,−3,…,84}, and designed minimum distance d ≥ |I|+1 = 90 [i]
- linear OA(2210, 255, F2, 86) (dual of [255, 45, 87]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,86], and designed minimum distance d ≥ |I|+1 = 87 [i]
- linear OA(2219, 255, F2, 91) (dual of [255, 36, 92]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−4,−3,…,86}, and designed minimum distance d ≥ |I|+1 = 92 [i]
- linear OA(2208, 255, F2, 84) (dual of [255, 47, 85]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,84], and designed minimum distance d ≥ |I|+1 = 85 [i]
- 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
- linear OA(21, 3, F2, 1) (dual of [3, 2, 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 (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(2221, 268, F2, 87) (dual of [268, 47, 88]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2221, 268, F2, 86) (dual of [268, 47, 87]-code) | [i] | ||
| 3 | Linear OA(2221, 268, F2, 85) (dual of [268, 47, 86]-code) | [i] | ||
| 4 | Linear OA(2221, 268, F2, 84) (dual of [268, 47, 85]-code) | [i] | ||
| 5 | Linear OA(2221, 268, F2, 83) (dual of [268, 47, 84]-code) | [i] | ||
| 6 | Linear OA(2221, 268, F2, 82) (dual of [268, 47, 83]-code) | [i] | ||
| 7 | Linear OA(2221, 268, F2, 81) (dual of [268, 47, 82]-code) | [i] | ||
| 8 | Linear OA(2221, 268, F2, 80) (dual of [268, 47, 81]-code) | [i] | ||
| 9 | Linear OA(2230, 277, F2, 88) (dual of [277, 47, 89]-code) | [i] | Code Embedding in Larger Space | |
| 10 | Linear OA(2231, 278, F2, 88) (dual of [278, 47, 89]-code) | [i] | ||
| 11 | Linear OA(2232, 279, F2, 88) (dual of [279, 47, 89]-code) | [i] | ||
| 12 | Linear OA(2222, 269, F2, 89) (dual of [269, 47, 90]-code) | [i] | Adding a Parity Check Bit | |
| 13 | Linear OA(2237, 285, F2, 88) (dual of [285, 48, 89]-code) | [i] | Construction X with Varšamov Bound | |
| 14 | Linear OA(2245, 294, F2, 88) (dual of [294, 49, 89]-code) | [i] | ||
| 15 | Linear OA(2258, 311, F2, 88) (dual of [311, 53, 89]-code) | [i] | ||
| 16 | Linear OOA(2221, 134, F2, 2, 88) (dual of [(134, 2), 47, 89]-NRT-code) | [i] | OOA Folding | |
| 17 | Linear OOA(2221, 89, F2, 3, 88) (dual of [(89, 3), 46, 89]-NRT-code) | [i] | ||