Information on Result #2175259
Linear OA(2260, 1096, F2, 49) (dual of [1096, 836, 50]-code), using adding a parity check bit based on linear OA(2259, 1095, F2, 48) (dual of [1095, 836, 49]-code), using
- construction XX applied to C1 = C([991,10]), C2 = C([985,4]), C3 = C1 + C2 = C([991,4]), and C∩ = C1 ∩ C2 = C([985,10]) [i] based on
- linear OA(2211, 1023, F2, 43) (dual of [1023, 812, 44]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−32,−31,…,10}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(2206, 1023, F2, 43) (dual of [1023, 817, 44]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−38,−37,…,4}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(2236, 1023, F2, 49) (dual of [1023, 787, 50]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−38,−37,…,10}, and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(2181, 1023, F2, 37) (dual of [1023, 842, 38]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−32,−31,…,4}, and designed minimum distance d ≥ |I|+1 = 38 [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(2260, 1096, F2, 48) (dual of [1096, 836, 49]-code) | [i] | Strength Reduction | |
| 2 | Linear OOA(2260, 548, F2, 2, 49) (dual of [(548, 2), 836, 50]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2260, 365, F2, 3, 49) (dual of [(365, 3), 835, 50]-NRT-code) | [i] | ||
| 4 | Linear OOA(2260, 274, F2, 4, 49) (dual of [(274, 4), 836, 50]-NRT-code) | [i] | ||
| 5 | Linear OOA(2260, 219, F2, 5, 49) (dual of [(219, 5), 835, 50]-NRT-code) | [i] | ||