Information on Result #805462
Linear OOA(234, 136, F2, 2, 8) (dual of [(136, 2), 238, 9]-NRT-code), using OOA 2-folding based on linear OA(234, 272, F2, 8) (dual of [272, 238, 9]-code), using
- 1 times truncation [i] based on linear OA(235, 273, F2, 9) (dual of [273, 238, 10]-code), using
- construction XX applied to C1 = C([253,4]), C2 = C([0,6]), C3 = C1 + C2 = C([0,4]), and C∩ = C1 ∩ C2 = C([253,6]) [i] based on
- linear OA(225, 255, F2, 7) (dual of [255, 230, 8]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,4}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(225, 255, F2, 7) (dual of [255, 230, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(233, 255, F2, 9) (dual of [255, 222, 10]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,6}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(217, 255, F2, 5) (dual of [255, 238, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(21, 9, F2, 1) (dual of [9, 8, 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, 9, F2, 1) (dual of [9, 8, 2]-code) (see above)
- construction XX applied to C1 = C([253,4]), C2 = C([0,6]), C3 = C1 + C2 = C([0,4]), and C∩ = C1 ∩ C2 = C([253,6]) [i] based on
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 OOA(2218, 4194437, F2, 2, 16) (dual of [(4194437, 2), 8388656, 17]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(2219, 4194437, F2, 2, 17) (dual of [(4194437, 2), 8388655, 18]-NRT-code) | [i] | ||
| 3 | Linear OOA(234, 136, F2, 3, 8) (dual of [(136, 3), 374, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(234, 136, F2, 4, 8) (dual of [(136, 4), 510, 9]-NRT-code) | [i] | ||
| 5 | Linear OOA(234, 136, F2, 5, 8) (dual of [(136, 5), 646, 9]-NRT-code) | [i] | ||
| 6 | Linear OOA(234, 136, F2, 6, 8) (dual of [(136, 6), 782, 9]-NRT-code) | [i] | ||
| 7 | Linear OOA(234, 136, F2, 7, 8) (dual of [(136, 7), 918, 9]-NRT-code) | [i] | ||