Information on Result #1018713
Linear OOA(8173, 2973351, F81, 3, 14) (dual of [(2973351, 3), 8919980, 15]-NRT-code), using (u, u+v)-construction based on
- linear OOA(8120, 177150, F81, 3, 7) (dual of [(177150, 3), 531430, 8]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8120, 531450, F81, 7) (dual of [531450, 531430, 8]-code), using
- construction X4 applied to C([0,3]) ⊂ C([0,2]) [i] based on
- linear OA(8119, 531442, F81, 7) (dual of [531442, 531423, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(8113, 531442, F81, 5) (dual of [531442, 531429, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(817, 8, F81, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,81)), using
- dual of repetition code with length 8 [i]
- linear OA(811, 8, F81, 1) (dual of [8, 7, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, 81, F81, 1) (dual of [81, 80, 2]-code), using
- Reed–Solomon code RS(80,81) [i]
- discarding factors / shortening the dual code based on linear OA(811, 81, F81, 1) (dual of [81, 80, 2]-code), using
- construction X4 applied to C([0,3]) ⊂ C([0,2]) [i] based on
- OOA 3-folding [i] based on linear OA(8120, 531450, F81, 7) (dual of [531450, 531430, 8]-code), using
- linear OOA(8153, 2796201, F81, 3, 14) (dual of [(2796201, 3), 8388550, 15]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8153, large, F81, 14) (dual of [large, large−53, 15]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- OOA 3-folding [i] based on linear OA(8153, large, F81, 14) (dual of [large, large−53, 15]-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(8174, 2973351, F81, 3, 14) (dual of [(2973351, 3), 8919979, 15]-NRT-code) | [i] | OOA Duplication | |