Information on Result #905287
Linear OOA(12878, 8493, F128, 2, 28) (dual of [(8493, 2), 16908, 29]-NRT-code), using (u, u+v)-construction based on
- linear OOA(12823, 300, F128, 2, 14) (dual of [(300, 2), 577, 15]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(1288, 150, F128, 2, 7) (dual of [(150, 2), 292, 8]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,292P) [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- linear OOA(12815, 150, F128, 2, 14) (dual of [(150, 2), 285, 15]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,285P) [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150 (see above)
- linear OOA(1288, 150, F128, 2, 7) (dual of [(150, 2), 292, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(12855, 8193, F128, 2, 28) (dual of [(8193, 2), 16331, 29]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12855, 16386, F128, 28) (dual of [16386, 16331, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(26) [i] based on
- 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(12853, 16384, F128, 27) (dual of [16384, 16331, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [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(27) ⊂ Ce(26) [i] based on
- OOA 2-folding [i] based on linear OA(12855, 16386, F128, 28) (dual of [16386, 16331, 29]-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, 4246, F128, 4, 28) (dual of [(4246, 4), 16906, 29]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(12878, 1213, F128, 30, 28) (dual of [(1213, 30), 36312, 29]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |