Information on Result #672586
Linear OA(2227, 32784, F2, 31) (dual of [32784, 32557, 32]-code), using construction X applied to Ce(30) ⊂ Ce(28) based on
- linear OA(2226, 32768, F2, 31) (dual of [32768, 32542, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2211, 32768, F2, 29) (dual of [32768, 32557, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(21, 16, F2, 1) (dual of [16, 15, 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(2227, 32784, F2, 30) (dual of [32784, 32557, 31]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2228, 32785, F2, 31) (dual of [32785, 32557, 32]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2229, 32786, F2, 31) (dual of [32786, 32557, 32]-code) | [i] | ||
| 4 | Linear OA(2230, 32787, F2, 31) (dual of [32787, 32557, 32]-code) | [i] | ||
| 5 | Linear OA(2231, 32788, F2, 31) (dual of [32788, 32557, 32]-code) | [i] | ||
| 6 | Linear OA(2226, 32783, F2, 30) (dual of [32783, 32557, 31]-code) | [i] | Truncation | |
| 7 | Linear OOA(2227, 16392, F2, 2, 31) (dual of [(16392, 2), 32557, 32]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(2227, 10928, F2, 3, 31) (dual of [(10928, 3), 32557, 32]-NRT-code) | [i] | ||
| 9 | Linear OOA(2227, 8196, F2, 4, 31) (dual of [(8196, 4), 32557, 32]-NRT-code) | [i] | ||
| 10 | Linear OOA(2227, 6556, F2, 5, 31) (dual of [(6556, 5), 32553, 32]-NRT-code) | [i] | ||
| 11 | Linear OOA(2227, 5464, F2, 6, 31) (dual of [(5464, 6), 32557, 32]-NRT-code) | [i] | ||
| 12 | Linear OOA(2227, 4683, F2, 7, 31) (dual of [(4683, 7), 32554, 32]-NRT-code) | [i] | ||
| 13 | Linear OOA(2227, 4098, F2, 8, 31) (dual of [(4098, 8), 32557, 32]-NRT-code) | [i] | ||
| 14 | Linear OOA(2227, 2185, F2, 31, 31) (dual of [(2185, 31), 67508, 32]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |