Information on Result #807581
Linear OOA(2159, 531, F2, 2, 30) (dual of [(531, 2), 903, 31]-NRT-code), using OOA 2-folding based on linear OA(2159, 1062, F2, 30) (dual of [1062, 903, 31]-code), using
- strength reduction [i] based on linear OA(2159, 1062, F2, 31) (dual of [1062, 903, 32]-code), using
- adding a parity check bit [i] based on linear OA(2158, 1061, F2, 30) (dual of [1061, 903, 31]-code), using
- construction XX applied to C1 = C([1019,24]), C2 = C([1,26]), C3 = C1 + C2 = C([1,24]), and C∩ = C1 ∩ C2 = C([1019,26]) [i] based on
- linear OA(2141, 1023, F2, 29) (dual of [1023, 882, 30]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,24}, and designed minimum distance d ≥ |I|+1 = 30 [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(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(2120, 1023, F2, 24) (dual of [1023, 903, 25]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [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([1019,24]), C2 = C([1,26]), C3 = C1 + C2 = C([1,24]), and C∩ = C1 ∩ C2 = C([1019,26]) [i] based on
- adding a parity check bit [i] based on linear OA(2158, 1061, F2, 30) (dual of [1061, 903, 31]-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(2161, 532, F2, 2, 30) (dual of [(532, 2), 903, 31]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(2160, 531, F2, 2, 30) (dual of [(531, 2), 902, 31]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2159, 531, F2, 3, 30) (dual of [(531, 3), 1434, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(2159, 531, F2, 4, 30) (dual of [(531, 4), 1965, 31]-NRT-code) | [i] | ||
| 5 | Linear OOA(2159, 531, F2, 5, 30) (dual of [(531, 5), 2496, 31]-NRT-code) | [i] | ||
| 6 | Linear OOA(2159, 531, F2, 6, 30) (dual of [(531, 6), 3027, 31]-NRT-code) | [i] | ||
| 7 | Linear OOA(2159, 531, F2, 7, 30) (dual of [(531, 7), 3558, 31]-NRT-code) | [i] | ||
| 8 | Linear OOA(2159, 531, F2, 8, 30) (dual of [(531, 8), 4089, 31]-NRT-code) | [i] | ||
| 9 | Digital (129, 159, 531)-net over F2 | [i] | ||