Information on Result #701810
Linear OA(2113, 299, F2, 27) (dual of [299, 186, 28]-code), using construction XX applied to C1 = C([251,18]), C2 = C([0,22]), C3 = C1 + C2 = C([0,18]), and C∩ = C1 ∩ C2 = C([251,22]) based on
- linear OA(285, 255, F2, 23) (dual of [255, 170, 24]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−4,−3,…,18}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(285, 255, F2, 23) (dual of [255, 170, 24]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(2101, 255, F2, 27) (dual of [255, 154, 28]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−4,−3,…,22}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(269, 255, F2, 19) (dual of [255, 186, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(26, 22, F2, 3) (dual of [22, 16, 4]-code or 22-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, 22, F2, 3) (dual of [22, 16, 4]-code or 22-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(2112, 298, F2, 26) (dual of [298, 186, 27]-code) | [i] | Truncation | |
| 2 | Linear OOA(2113, 149, F2, 2, 27) (dual of [(149, 2), 185, 28]-NRT-code) | [i] | OOA Folding | |