Information on Result #1699709
Linear OOA(2161, 532, F2, 8, 31) (dual of [(532, 8), 4095, 32]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2161, 532, F2, 2, 31) (dual of [(532, 2), 903, 32]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2159, 531, F2, 2, 31) (dual of [(531, 2), 903, 32]-NRT-code), using
- OOA 2-folding [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
- OOA 2-folding [i] based on linear OA(2159, 1062, F2, 31) (dual of [1062, 903, 32]-code), using
Mode: 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(2162, 532, F2, 8, 31) (dual of [(532, 8), 4094, 32]-NRT-code) | [i] | OOA Duplication | |