Information on Result #2175119
Linear OA(2189, 1047, F2, 39) (dual of [1047, 858, 40]-code), using adding a parity check bit based on linear OA(2188, 1046, F2, 38) (dual of [1046, 858, 39]-code), using
- construction XX applied to C1 = C([1021,34]), C2 = C([1,36]), C3 = C1 + C2 = C([1,34]), and C∩ = C1 ∩ C2 = C([1021,36]) [i] based on
- 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 = {−2,−1,…,34}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(2175, 1023, F2, 36) (dual of [1023, 848, 37]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [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 = {−2,−1,…,36}, and designed minimum distance d ≥ |I|+1 = 40 [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(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
- 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 (see above)
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(2189, 1047, F2, 38) (dual of [1047, 858, 39]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2190, 1048, F2, 39) (dual of [1048, 858, 40]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OOA(2189, 523, F2, 2, 39) (dual of [(523, 2), 857, 40]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(2189, 349, F2, 3, 39) (dual of [(349, 3), 858, 40]-NRT-code) | [i] | ||