Information on Result #809451
Linear OOA(2250, 539, F2, 2, 49) (dual of [(539, 2), 828, 50]-NRT-code), using OOA 2-folding based on linear OA(2250, 1078, F2, 49) (dual of [1078, 828, 50]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2249, 1077, F2, 49) (dual of [1077, 828, 50]-code), using
- adding a parity check bit [i] based on linear OA(2248, 1076, F2, 48) (dual of [1076, 828, 49]-code), using
- construction XX applied to C1 = C([1019,40]), C2 = C([1,44]), C3 = C1 + C2 = C([1,40]), and C∩ = C1 ∩ C2 = C([1019,44]) [i] based on
- linear OA(2216, 1023, F2, 45) (dual of [1023, 807, 46]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,40}, and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(2215, 1023, F2, 44) (dual of [1023, 808, 45]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(2236, 1023, F2, 49) (dual of [1023, 787, 50]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,44}, and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(2195, 1023, F2, 40) (dual of [1023, 828, 41]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(26, 27, F2, 3) (dual of [27, 21, 4]-code or 27-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, 26, F2, 3) (dual of [26, 20, 4]-code or 26-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)
- construction XX applied to C1 = C([1019,40]), C2 = C([1,44]), C3 = C1 + C2 = C([1,40]), and C∩ = C1 ∩ C2 = C([1019,44]) [i] based on
- adding a parity check bit [i] based on linear OA(2248, 1076, F2, 48) (dual of [1076, 828, 49]-code), 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 OOA(2250, 539, F2, 2, 48) (dual of [(539, 2), 828, 49]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2252, 540, F2, 2, 49) (dual of [(540, 2), 828, 50]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 3 | Linear OOA(2251, 539, F2, 2, 49) (dual of [(539, 2), 827, 50]-NRT-code) | [i] | OOA Duplication | |