Information on Result #904473
Linear OOA(8179, 4460105, F81, 2, 15) (dual of [(4460105, 2), 8920131, 16]-NRT-code), using (u, u+v)-construction based on
- linear OOA(8122, 265804, F81, 2, 7) (dual of [(265804, 2), 531586, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(813, 82, F81, 2, 3) (dual of [(82, 2), 161, 4]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;161,81) [i]
- linear OOA(8119, 265722, F81, 2, 7) (dual of [(265722, 2), 531425, 8]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8119, 531444, F81, 7) (dual of [531444, 531425, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(8119, 531441, F81, 7) (dual of [531441, 531422, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(8116, 531441, F81, 6) (dual of [531441, 531425, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(810, 3, F81, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- OOA 2-folding [i] based on linear OA(8119, 531444, F81, 7) (dual of [531444, 531425, 8]-code), using
- linear OOA(813, 82, F81, 2, 3) (dual of [(82, 2), 161, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(8157, 4194301, F81, 2, 15) (dual of [(4194301, 2), 8388545, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8157, 8388602, F81, 15) (dual of [8388602, 8388545, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(8157, large, F81, 15) (dual of [large, large−57, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(8157, large, F81, 15) (dual of [large, large−57, 16]-code), using
- OOA 2-folding [i] based on linear OA(8157, 8388602, F81, 15) (dual of [8388602, 8388545, 16]-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(8179, 2230052, F81, 4, 15) (dual of [(2230052, 4), 8920129, 16]-NRT-code) | [i] | OOA Folding | |