Information on Result #905110
Linear OOA(12856, 8493, F128, 2, 20) (dual of [(8493, 2), 16930, 21]-NRT-code), using (u, u+v)-construction based on
- linear OOA(12817, 300, F128, 2, 10) (dual of [(300, 2), 583, 11]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(1286, 150, F128, 2, 5) (dual of [(150, 2), 294, 6]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,294P) [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- linear OOA(12811, 150, F128, 2, 10) (dual of [(150, 2), 289, 11]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,289P) [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150 (see above)
- linear OOA(1286, 150, F128, 2, 5) (dual of [(150, 2), 294, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(12839, 8193, F128, 2, 20) (dual of [(8193, 2), 16347, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12839, 16386, F128, 20) (dual of [16386, 16347, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- linear OA(12839, 16384, F128, 20) (dual of [16384, 16345, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(12837, 16384, F128, 19) (dual of [16384, 16347, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(19) ⊂ Ce(18) [i] based on
- OOA 2-folding [i] based on linear OA(12839, 16386, F128, 20) (dual of [16386, 16347, 21]-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(12856, 4246, F128, 4, 20) (dual of [(4246, 4), 16928, 21]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(12856, 1698, F128, 22, 20) (dual of [(1698, 22), 37300, 21]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |