Information on Result #807121
Linear OOA(2139, 531, F2, 2, 26) (dual of [(531, 2), 923, 27]-NRT-code), using OOA 2-folding based on linear OA(2139, 1062, F2, 26) (dual of [1062, 923, 27]-code), using
- strength reduction [i] based on linear OA(2139, 1062, F2, 27) (dual of [1062, 923, 28]-code), using
- adding a parity check bit [i] based on linear OA(2138, 1061, F2, 26) (dual of [1061, 923, 27]-code), using
- construction XX applied to C1 = C([1019,20]), C2 = C([1,22]), C3 = C1 + C2 = C([1,20]), and C∩ = C1 ∩ C2 = C([1019,22]) [i] based on
- linear OA(2121, 1023, F2, 25) (dual of [1023, 902, 26]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,20}, and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(2110, 1023, F2, 22) (dual of [1023, 913, 23]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2131, 1023, F2, 27) (dual of [1023, 892, 28]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,22}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(2100, 1023, F2, 20) (dual of [1023, 923, 21]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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([1019,20]), C2 = C([1,22]), C3 = C1 + C2 = C([1,20]), and C∩ = C1 ∩ C2 = C([1019,22]) [i] based on
- adding a parity check bit [i] based on linear OA(2138, 1061, F2, 26) (dual of [1061, 923, 27]-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(2141, 532, F2, 2, 26) (dual of [(532, 2), 923, 27]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(2140, 531, F2, 2, 26) (dual of [(531, 2), 922, 27]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2139, 531, F2, 3, 26) (dual of [(531, 3), 1454, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(2139, 531, F2, 4, 26) (dual of [(531, 4), 1985, 27]-NRT-code) | [i] | ||
| 5 | Linear OOA(2139, 531, F2, 5, 26) (dual of [(531, 5), 2516, 27]-NRT-code) | [i] | ||
| 6 | Linear OOA(2139, 531, F2, 6, 26) (dual of [(531, 6), 3047, 27]-NRT-code) | [i] | ||
| 7 | Linear OOA(2139, 531, F2, 7, 26) (dual of [(531, 7), 3578, 27]-NRT-code) | [i] | ||
| 8 | Linear OOA(2139, 531, F2, 8, 26) (dual of [(531, 8), 4109, 27]-NRT-code) | [i] | ||
| 9 | Digital (113, 139, 531)-net over F2 | [i] | ||