Information on Result #2226161
Linear OA(2182, 1054, F2, 36) (dual of [1054, 872, 37]-code), using 1 times truncation based on linear OA(2183, 1055, F2, 37) (dual of [1055, 872, 38]-code), using
- construction XX applied to C1 = C([989,0]), C2 = C([993,2]), C3 = C1 + C2 = C([993,0]), and C∩ = C1 ∩ C2 = C([989,2]) [i] based on
- linear OA(2166, 1023, F2, 35) (dual of [1023, 857, 36]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−34,−33,…,0}, and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(2161, 1023, F2, 33) (dual of [1023, 862, 34]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−30,−29,…,2}, and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(2176, 1023, F2, 37) (dual of [1023, 847, 38]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−34,−33,…,2}, and designed minimum distance d ≥ |I|+1 = 38 [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 = {−30,−29,…,0}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(26, 21, F2, 3) (dual of [21, 15, 4]-code or 21-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
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(2182, 527, F2, 2, 36) (dual of [(527, 2), 872, 37]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(2182, 351, F2, 3, 36) (dual of [(351, 3), 871, 37]-NRT-code) | [i] | ||
| 3 | Linear OOA(2182, 263, F2, 4, 36) (dual of [(263, 4), 870, 37]-NRT-code) | [i] | ||