Information on Result #2175233
Linear OA(2250, 1096, F2, 47) (dual of [1096, 846, 48]-code), using adding a parity check bit based on linear OA(2249, 1095, F2, 46) (dual of [1095, 846, 47]-code), using
- construction XX applied to C1 = C([991,8]), C2 = C([985,2]), C3 = C1 + C2 = C([991,2]), and C∩ = C1 ∩ C2 = C([985,8]) [i] based on
- linear OA(2201, 1023, F2, 41) (dual of [1023, 822, 42]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−32,−31,…,8}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(2196, 1023, F2, 41) (dual of [1023, 827, 42]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−38,−37,…,2}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(2226, 1023, F2, 47) (dual of [1023, 797, 48]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−38,−37,…,8}, and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(2171, 1023, F2, 35) (dual of [1023, 852, 36]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−32,−31,…,2}, and designed minimum distance d ≥ |I|+1 = 36 [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(211, 36, F2, 4) (dual of [36, 25, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(211, 44, F2, 4) (dual of [44, 33, 5]-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 OA(2250, 1096, F2, 46) (dual of [1096, 846, 47]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2251, 1097, F2, 47) (dual of [1097, 846, 48]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2252, 1098, F2, 47) (dual of [1098, 846, 48]-code) | [i] | ||
| 4 | Linear OOA(2250, 548, F2, 2, 47) (dual of [(548, 2), 846, 48]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(2250, 365, F2, 3, 47) (dual of [(365, 3), 845, 48]-NRT-code) | [i] | ||
| 6 | Linear OOA(2250, 274, F2, 4, 47) (dual of [(274, 4), 846, 48]-NRT-code) | [i] | ||
| 7 | Linear OOA(2250, 219, F2, 5, 47) (dual of [(219, 5), 845, 48]-NRT-code) | [i] | ||