Information on Result #1019442
Linear OOA(12851, 5741, F128, 3, 19) (dual of [(5741, 3), 17172, 20]-NRT-code), using (u, u+v)-construction based on
- linear OOA(12814, 279, F128, 3, 9) (dual of [(279, 3), 823, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(1284, 129, F128, 3, 4) (dual of [(129, 3), 383, 5]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;383,128) [i]
- linear OOA(12810, 150, F128, 3, 9) (dual of [(150, 3), 440, 10]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(3;F,440P) [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- linear OOA(1284, 129, F128, 3, 4) (dual of [(129, 3), 383, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(12837, 5462, F128, 3, 19) (dual of [(5462, 3), 16349, 20]-NRT-code), using
- OOA 3-folding [i] based on linear OA(12837, 16386, F128, 19) (dual of [16386, 16349, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- 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(12835, 16384, F128, 18) (dual of [16384, 16349, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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(18) ⊂ Ce(17) [i] based on
- OOA 3-folding [i] based on linear OA(12837, 16386, F128, 19) (dual of [16386, 16349, 20]-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(12851, 1913, F128, 21, 19) (dual of [(1913, 21), 40122, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |