Information on Result #1014690
Linear OOA(8160, 5595134, F8, 3, 17) (dual of [(5595134, 3), 16785242, 18]-NRT-code), using (u, u+v)-construction based on
- linear OOA(830, 2732, F8, 3, 8) (dual of [(2732, 3), 8166, 9]-NRT-code), using
- OOA 3-folding [i] based on linear OA(830, 8196, F8, 8) (dual of [8196, 8166, 9]-code), using
- trace code [i] based on linear OA(6415, 4098, F64, 8) (dual of [4098, 4083, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(6415, 4096, F64, 8) (dual of [4096, 4081, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(6413, 4096, F64, 7) (dual of [4096, 4083, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(640, 2, F64, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- trace code [i] based on linear OA(6415, 4098, F64, 8) (dual of [4098, 4083, 9]-code), using
- OOA 3-folding [i] based on linear OA(830, 8196, F8, 8) (dual of [8196, 8166, 9]-code), using
- linear OOA(8130, 5592402, F8, 3, 17) (dual of [(5592402, 3), 16777076, 18]-NRT-code), using
- trace code [i] based on linear OOA(6465, 2796201, F64, 3, 17) (dual of [(2796201, 3), 8388538, 18]-NRT-code), using
- OOA 3-folding [i] based on linear OA(6465, large, F64, 17) (dual of [large, large−65, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(6465, large, F64, 17) (dual of [large, large−65, 18]-code), using
- trace code [i] based on linear OOA(6465, 2796201, F64, 3, 17) (dual of [(2796201, 3), 8388538, 18]-NRT-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(8161, 5595134, F8, 3, 17) (dual of [(5595134, 3), 16785241, 18]-NRT-code) | [i] | OOA Duplication | |