Information on Result #2175113
Linear OA(2184, 1057, F2, 37) (dual of [1057, 873, 38]-code), using adding a parity check bit based on linear OA(2183, 1056, F2, 36) (dual of [1056, 873, 37]-code), using
- construction XX applied to C1 = C([989,1022]), C2 = C([993,2]), C3 = C1 + C2 = C([993,1022]), and C∩ = C1 ∩ C2 = C([989,2]) [i] based on
- linear OA(2165, 1023, F2, 34) (dual of [1023, 858, 35]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−34,−33,…,−1}, and designed minimum distance d ≥ |I|+1 = 35 [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(2150, 1023, F2, 30) (dual of [1023, 873, 31]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−30,−29,…,−1}, and designed minimum distance d ≥ |I|+1 = 31 [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, 12, F2, 1) (dual of [12, 11, 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 OA(2184, 1057, F2, 36) (dual of [1057, 873, 37]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2185, 1058, F2, 37) (dual of [1058, 873, 38]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2187, 1060, F2, 37) (dual of [1060, 873, 38]-code) | [i] | ||
| 4 | Linear OOA(2184, 528, F2, 2, 37) (dual of [(528, 2), 872, 38]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(2184, 352, F2, 3, 37) (dual of [(352, 3), 872, 38]-NRT-code) | [i] | ||
| 6 | Linear OOA(2184, 264, F2, 4, 37) (dual of [(264, 4), 872, 38]-NRT-code) | [i] | ||
| 7 | Linear OOA(2184, 176, F2, 6, 37) (dual of [(176, 6), 872, 38]-NRT-code) | [i] | ||
| 8 | Linear OOA(2184, 151, F2, 7, 37) (dual of [(151, 7), 873, 38]-NRT-code) | [i] | ||
| 9 | Linear OOA(2184, 132, F2, 8, 37) (dual of [(132, 8), 872, 38]-NRT-code) | [i] | ||