Information on Result #702800
Linear OA(2164, 1070, F2, 30) (dual of [1070, 906, 31]-code), using construction XX applied to C1 = C([1017,22]), C2 = C([1,24]), C3 = C1 + C2 = C([1,22]), and C∩ = C1 ∩ C2 = C([1017,24]) 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 = {−6,−5,…,22}, and designed minimum distance d ≥ |I|+1 = 30 [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(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 = {−6,−5,…,24}, and designed minimum distance d ≥ |I|+1 = 32 [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(212, 36, F2, 5) (dual of [36, 24, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(212, 38, F2, 5) (dual of [38, 26, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(2) [i] based on
- linear OA(211, 32, F2, 5) (dual of [32, 21, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 31 = 25−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 31 = 25−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(21, 6, F2, 1) (dual of [6, 5, 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 X applied to Ce(4) ⊂ Ce(2) [i] based on
- discarding factors / shortening the dual code based on linear OA(212, 38, F2, 5) (dual of [38, 26, 6]-code), 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)
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(2164, 603, F2, 2, 30) (dual of [(603, 2), 1042, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2164, 603, F2, 3, 30) (dual of [(603, 3), 1645, 31]-NRT-code) | [i] | ||
| 3 | Linear OOA(2164, 603, F2, 4, 30) (dual of [(603, 4), 2248, 31]-NRT-code) | [i] | ||
| 4 | Linear OOA(2164, 603, F2, 5, 30) (dual of [(603, 5), 2851, 31]-NRT-code) | [i] | ||
| 5 | Linear OOA(2164, 603, F2, 6, 30) (dual of [(603, 6), 3454, 31]-NRT-code) | [i] | ||
| 6 | Linear OOA(2164, 603, F2, 7, 30) (dual of [(603, 7), 4057, 31]-NRT-code) | [i] | ||
| 7 | Linear OOA(2164, 603, F2, 8, 30) (dual of [(603, 8), 4660, 31]-NRT-code) | [i] | ||
| 8 | Digital (134, 164, 603)-net over F2 | [i] | ||