Information on Result #807690
Linear OOA(2154, 523, F2, 2, 31) (dual of [(523, 2), 892, 32]-NRT-code), using OOA 2-folding based on linear OA(2154, 1046, F2, 31) (dual of [1046, 892, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(2154, 1047, F2, 31) (dual of [1047, 893, 32]-code), using
- adding a parity check bit [i] based on linear OA(2153, 1046, F2, 30) (dual of [1046, 893, 31]-code), using
- construction XX applied to C1 = C([1021,26]), C2 = C([1,28]), C3 = C1 + C2 = C([1,26]), and C∩ = C1 ∩ C2 = C([1021,28]) [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 = {−2,−1,…,26}, and designed minimum distance d ≥ |I|+1 = 30 [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(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 = {−2,−1,…,28}, and designed minimum distance d ≥ |I|+1 = 32 [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(21, 12, F2, 1) (dual of [12, 11, 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, 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 (see above)
- construction XX applied to C1 = C([1021,26]), C2 = C([1,28]), C3 = C1 + C2 = C([1,26]), and C∩ = C1 ∩ C2 = C([1021,28]) [i] based on
- adding a parity check bit [i] based on linear OA(2153, 1046, F2, 30) (dual of [1046, 893, 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(2154, 523, F2, 2, 30) (dual of [(523, 2), 892, 31]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2154, 448, F2, 3, 31) (dual of [(448, 3), 1190, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(2154, 448, F2, 4, 31) (dual of [(448, 4), 1638, 32]-NRT-code) | [i] | ||
| 4 | Linear OOA(2154, 448, F2, 5, 31) (dual of [(448, 5), 2086, 32]-NRT-code) | [i] | ||
| 5 | Linear OOA(2154, 448, F2, 6, 31) (dual of [(448, 6), 2534, 32]-NRT-code) | [i] | ||
| 6 | Linear OOA(2154, 448, F2, 7, 31) (dual of [(448, 7), 2982, 32]-NRT-code) | [i] | ||
| 7 | Linear OOA(2154, 448, F2, 8, 31) (dual of [(448, 8), 3430, 32]-NRT-code) | [i] | ||
| 8 | Digital (123, 154, 448)-net over F2 | [i] | ||