Information on Result #2479577
Linear OOA(2152, 532, F2, 2, 29) (dual of [(532, 2), 912, 30]-NRT-code), using 21 times duplication based on linear OOA(2151, 532, F2, 2, 29) (dual of [(532, 2), 913, 30]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2149, 531, F2, 2, 29) (dual of [(531, 2), 913, 30]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2149, 1062, F2, 29) (dual of [1062, 913, 30]-code), using
- adding a parity check bit [i] based on linear OA(2148, 1061, F2, 28) (dual of [1061, 913, 29]-code), using
- construction XX applied to C1 = C([1019,22]), C2 = C([1,24]), C3 = C1 + C2 = C([1,22]), and C∩ = C1 ∩ C2 = C([1019,24]) [i] based on
- 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(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(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(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(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([1019,22]), C2 = C([1,24]), C3 = C1 + C2 = C([1,22]), and C∩ = C1 ∩ C2 = C([1019,24]) [i] based on
- adding a parity check bit [i] based on linear OA(2148, 1061, F2, 28) (dual of [1061, 913, 29]-code), using
- OOA 2-folding [i] based on linear OA(2149, 1062, F2, 29) (dual of [1062, 913, 30]-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(2152, 532, F2, 3, 29) (dual of [(532, 3), 1444, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2152, 532, F2, 4, 29) (dual of [(532, 4), 1976, 30]-NRT-code) | [i] | ||
| 3 | Linear OOA(2152, 532, F2, 5, 29) (dual of [(532, 5), 2508, 30]-NRT-code) | [i] | ||
| 4 | Linear OOA(2152, 532, F2, 6, 29) (dual of [(532, 6), 3040, 30]-NRT-code) | [i] | ||
| 5 | Linear OOA(2152, 532, F2, 7, 29) (dual of [(532, 7), 3572, 30]-NRT-code) | [i] | ||
| 6 | Linear OOA(2152, 532, F2, 8, 29) (dual of [(532, 8), 4104, 30]-NRT-code) | [i] | ||
| 7 | Digital (123, 152, 532)-net over F2 | [i] | ||