Information on Result #2479898
Linear OOA(2170, 531, F2, 2, 33) (dual of [(531, 2), 892, 34]-NRT-code), using 21 times duplication based on linear OOA(2169, 531, F2, 2, 33) (dual of [(531, 2), 893, 34]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2169, 1062, F2, 33) (dual of [1062, 893, 34]-code), using
- adding a parity check bit [i] based on linear OA(2168, 1061, F2, 32) (dual of [1061, 893, 33]-code), using
- construction XX applied to C1 = C([1019,26]), C2 = C([1,28]), C3 = C1 + C2 = C([1,26]), and C∩ = C1 ∩ C2 = C([1019,28]) [i] based on
- linear OA(2151, 1023, F2, 31) (dual of [1023, 872, 32]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,26}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(2140, 1023, F2, 28) (dual of [1023, 883, 29]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(2161, 1023, F2, 33) (dual of [1023, 862, 34]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,28}, and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(2130, 1023, F2, 26) (dual of [1023, 893, 27]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [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(21, 11, F2, 1) (dual of [11, 10, 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
- construction XX applied to C1 = C([1019,26]), C2 = C([1,28]), C3 = C1 + C2 = C([1,26]), and C∩ = C1 ∩ C2 = C([1019,28]) [i] based on
- adding a parity check bit [i] based on linear OA(2168, 1061, F2, 32) (dual of [1061, 893, 33]-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(2170, 531, F2, 3, 33) (dual of [(531, 3), 1423, 34]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2170, 531, F2, 4, 33) (dual of [(531, 4), 1954, 34]-NRT-code) | [i] | ||
| 3 | Linear OOA(2170, 531, F2, 5, 33) (dual of [(531, 5), 2485, 34]-NRT-code) | [i] | ||
| 4 | Linear OOA(2170, 531, F2, 6, 33) (dual of [(531, 6), 3016, 34]-NRT-code) | [i] | ||
| 5 | Linear OOA(2170, 531, F2, 7, 33) (dual of [(531, 7), 3547, 34]-NRT-code) | [i] | ||
| 6 | Linear OOA(2170, 531, F2, 8, 33) (dual of [(531, 8), 4078, 34]-NRT-code) | [i] | ||
| 7 | Digital (137, 170, 531)-net over F2 | [i] | ||