Information on Result #2175015
Linear OA(2134, 1047, F2, 27) (dual of [1047, 913, 28]-code), using adding a parity check bit based on linear OA(2133, 1046, F2, 26) (dual of [1046, 913, 27]-code), using
- construction XX applied to C1 = C([1021,22]), C2 = C([1,24]), C3 = C1 + C2 = C([1,22]), and C∩ = C1 ∩ C2 = C([1021,24]) [i] based on
- linear OA(2121, 1023, F2, 25) (dual of [1023, 902, 26]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,22}, and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(2120, 1023, F2, 24) (dual of [1023, 903, 25]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(2131, 1023, F2, 27) (dual of [1023, 892, 28]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,24}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(2110, 1023, F2, 22) (dual of [1023, 913, 23]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(2134, 1047, F2, 26) (dual of [1047, 913, 27]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2135, 1048, F2, 27) (dual of [1048, 913, 28]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OOA(2134, 523, F2, 2, 27) (dual of [(523, 2), 912, 28]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(2134, 349, F2, 3, 27) (dual of [(349, 3), 913, 28]-NRT-code) | [i] | ||