Information on Result #611270
Linear OA(285, 128, F2, 31) (dual of [128, 43, 32]-code), using construction X applied to C([0,28]) ⊂ C([1,28]) based on
- linear OA(285, 127, F2, 31) (dual of [127, 42, 32]-code), using the expurgated primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,28], and minimum distance d ≥ 32 (sporadic result) and all weights a multiple of 2 because the code is contained in its dual [i]
- linear OA(284, 127, F2, 30) (dual of [127, 43, 31]-code), using the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,28], and minimum distance d ≥ 31 (sporadic result) [i]
- linear OA(20, 1, F2, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(20, s, F2, 0) (dual of [s, s, 1]-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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(285, 128, F2, 30) (dual of [128, 43, 31]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(285, 128, F2, 29) (dual of [128, 43, 30]-code) | [i] | ||
| 3 | Linear OA(286, 129, F2, 31) (dual of [129, 43, 32]-code) | [i] | Code Embedding in Larger Space | |
| 4 | Linear OA(287, 130, F2, 31) (dual of [130, 43, 32]-code) | [i] | ||
| 5 | Linear OA(283, 126, F2, 29) (dual of [126, 43, 30]-code) | [i] | Truncation | |
| 6 | Linear OA(282, 125, F2, 28) (dual of [125, 43, 29]-code) | [i] | ||
| 7 | Linear OOA(285, 64, F2, 2, 31) (dual of [(64, 2), 43, 32]-NRT-code) | [i] | OOA Folding | |