Information on Result #673982
Linear OA(286, 136, F2, 29) (dual of [136, 50, 30]-code), using construction X applied to Ce(28) ⊂ Ce(26) based on
- linear OA(285, 128, F2, 29) (dual of [128, 43, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(278, 128, F2, 27) (dual of [128, 50, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(21, 8, F2, 1) (dual of [8, 7, 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.
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(286, 136, F2, 28) (dual of [136, 50, 29]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(287, 137, F2, 29) (dual of [137, 50, 30]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(285, 135, F2, 28) (dual of [135, 50, 29]-code) | [i] | Truncation | |
| 4 | Linear OOA(286, 68, F2, 2, 29) (dual of [(68, 2), 50, 30]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(286, 45, F2, 3, 29) (dual of [(45, 3), 49, 30]-NRT-code) | [i] | ||