Information on Result #2175132
Linear OA(2194, 1057, F2, 39) (dual of [1057, 863, 40]-code), using adding a parity check bit based on linear OA(2193, 1056, F2, 38) (dual of [1056, 863, 39]-code), using
- construction XX applied to C1 = C([1019,32]), C2 = C([1,34]), C3 = C1 + C2 = C([1,32]), and C∩ = C1 ∩ C2 = C([1019,34]) [i] based on
- 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 = {−4,−3,…,32}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(2165, 1023, F2, 34) (dual of [1023, 858, 35]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(2186, 1023, F2, 39) (dual of [1023, 837, 40]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,34}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(2160, 1023, F2, 32) (dual of [1023, 863, 33]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(26, 27, F2, 3) (dual of [27, 21, 4]-code or 27-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, 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
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(2194, 1057, F2, 38) (dual of [1057, 863, 39]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2195, 1058, F2, 39) (dual of [1058, 863, 40]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2196, 1059, F2, 39) (dual of [1059, 863, 40]-code) | [i] | ||
| 4 | Linear OOA(2194, 528, F2, 2, 39) (dual of [(528, 2), 862, 40]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(2194, 352, F2, 3, 39) (dual of [(352, 3), 862, 40]-NRT-code) | [i] | ||
| 6 | Linear OOA(2194, 264, F2, 4, 39) (dual of [(264, 4), 862, 40]-NRT-code) | [i] | ||
| 7 | Linear OOA(2194, 176, F2, 6, 39) (dual of [(176, 6), 862, 40]-NRT-code) | [i] | ||
| 8 | Linear OOA(2194, 151, F2, 7, 39) (dual of [(151, 7), 863, 40]-NRT-code) | [i] | ||
| 9 | Linear OOA(2194, 132, F2, 8, 39) (dual of [(132, 8), 862, 40]-NRT-code) | [i] | ||