Information on Result #905305
Linear OOA(12878, 8451, F128, 2, 29) (dual of [(8451, 2), 16824, 30]-NRT-code), using (u, u+v)-construction based on
- linear OOA(12821, 258, F128, 2, 14) (dual of [(258, 2), 495, 15]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(1287, 129, F128, 2, 7) (dual of [(129, 2), 251, 8]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;251,128) [i]
- linear OOA(12814, 129, F128, 2, 14) (dual of [(129, 2), 244, 15]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;244,128) [i]
- linear OOA(1287, 129, F128, 2, 7) (dual of [(129, 2), 251, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(12857, 8193, F128, 2, 29) (dual of [(8193, 2), 16329, 30]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12857, 16386, F128, 29) (dual of [16386, 16329, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(27) [i] based on
- linear OA(12857, 16384, F128, 29) (dual of [16384, 16327, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(12855, 16384, F128, 28) (dual of [16384, 16329, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(1280, 2, F128, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(28) ⊂ Ce(27) [i] based on
- OOA 2-folding [i] based on linear OA(12857, 16386, F128, 29) (dual of [16386, 16329, 30]-code), 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 OOA(12878, 4225, F128, 4, 29) (dual of [(4225, 4), 16822, 30]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(12878, 1207, F128, 30, 29) (dual of [(1207, 30), 36132, 30]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |