Information on Result #672386
Linear OA(2254, 262163, F2, 29) (dual of [262163, 261909, 30]-code), using construction X applied to Ce(28) ⊂ Ce(26) based on
- linear OA(2253, 262144, F2, 29) (dual of [262144, 261891, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(2235, 262144, F2, 27) (dual of [262144, 261909, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(21, 19, F2, 1) (dual of [19, 18, 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(2254, 262163, F2, 28) (dual of [262163, 261909, 29]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2255, 262164, F2, 29) (dual of [262164, 261909, 30]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2256, 262165, F2, 29) (dual of [262165, 261909, 30]-code) | [i] | ||
| 4 | Linear OA(2257, 262166, F2, 29) (dual of [262166, 261909, 30]-code) | [i] | ||
| 5 | Linear OA(2258, 262167, F2, 29) (dual of [262167, 261909, 30]-code) | [i] | ||
| 6 | Linear OA(2253, 262162, F2, 28) (dual of [262162, 261909, 29]-code) | [i] | Truncation | |
| 7 | Linear OOA(2254, 131081, F2, 2, 29) (dual of [(131081, 2), 261908, 30]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(2254, 87387, F2, 3, 29) (dual of [(87387, 3), 261907, 30]-NRT-code) | [i] | ||
| 9 | Linear OOA(2254, 65540, F2, 4, 29) (dual of [(65540, 4), 261906, 30]-NRT-code) | [i] | ||
| 10 | Linear OOA(2254, 52432, F2, 5, 29) (dual of [(52432, 5), 261906, 30]-NRT-code) | [i] | ||
| 11 | Linear OOA(2254, 43693, F2, 6, 29) (dual of [(43693, 6), 261904, 30]-NRT-code) | [i] | ||
| 12 | Linear OOA(2254, 37451, F2, 7, 29) (dual of [(37451, 7), 261903, 30]-NRT-code) | [i] | ||
| 13 | Linear OOA(2254, 32770, F2, 8, 29) (dual of [(32770, 8), 261906, 30]-NRT-code) | [i] | ||
| 14 | Linear OOA(2254, 18725, F2, 29, 29) (dual of [(18725, 29), 542771, 30]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |