Information on Result #1082558
Linear OOA(8180, 4194302, F81, 4, 14) (dual of [(4194302, 4), 16777128, 15]-NRT-code), using (u, u+v)-construction based on
- linear OOA(8125, 2796200, F81, 4, 7) (dual of [(2796200, 4), 11184775, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(8125, 8388601, F81, 7) (dual of [8388601, 8388576, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(8125, large, F81, 7) (dual of [large, large−25, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(8125, large, F81, 7) (dual of [large, large−25, 8]-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(8125, 8388601, F81, 7) (dual of [8388601, 8388576, 8]-code), using
- linear OOA(8155, 2097151, F81, 4, 14) (dual of [(2097151, 4), 8388549, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(8155, 4194302, F81, 2, 14) (dual of [(4194302, 2), 8388549, 15]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(8153, 4194301, F81, 2, 14) (dual of [(4194301, 2), 8388549, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8153, 8388602, F81, 14) (dual of [8388602, 8388549, 15]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(8153, large, F81, 14) (dual of [large, large−53, 15]-code), using
- OOA 2-folding [i] based on linear OA(8153, 8388602, F81, 14) (dual of [8388602, 8388549, 15]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(8153, 4194301, F81, 2, 14) (dual of [(4194301, 2), 8388549, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(8155, 4194302, F81, 2, 14) (dual of [(4194302, 2), 8388549, 15]-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(8181, 4194302, F81, 4, 14) (dual of [(4194302, 4), 16777127, 15]-NRT-code) | [i] | OOA Duplication | |