Information on Result #1014396
Linear OOA(8108, 5854548, F8, 3, 11) (dual of [(5854548, 3), 17563536, 12]-NRT-code), using (u, u+v)-construction based on
- linear OOA(826, 262146, F8, 3, 5) (dual of [(262146, 3), 786412, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(826, 524293, F8, 5) (dual of [524293, 524267, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(826, 524294, F8, 5) (dual of [524294, 524268, 6]-code), using
- trace code [i] based on linear OA(6413, 262147, F64, 5) (dual of [262147, 262134, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(6413, 262144, F64, 5) (dual of [262144, 262131, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(6410, 262144, F64, 4) (dual of [262144, 262134, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 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(4) ⊂ Ce(3) [i] based on
- trace code [i] based on linear OA(6413, 262147, F64, 5) (dual of [262147, 262134, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(826, 524294, F8, 5) (dual of [524294, 524268, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(826, 524293, F8, 5) (dual of [524293, 524267, 6]-code), using
- linear OOA(882, 5592402, F8, 3, 11) (dual of [(5592402, 3), 16777124, 12]-NRT-code), using
- trace code [i] based on linear OOA(6441, 2796201, F64, 3, 11) (dual of [(2796201, 3), 8388562, 12]-NRT-code), using
- OOA 3-folding [i] based on linear OA(6441, large, F64, 11) (dual of [large, large−41, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(6441, large, F64, 11) (dual of [large, large−41, 12]-code), using
- trace code [i] based on linear OOA(6441, 2796201, F64, 3, 11) (dual of [(2796201, 3), 8388562, 12]-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(8108, 2927273, F8, 15, 11) (dual of [(2927273, 15), 43908987, 12]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |