Information on Result #904439
Linear OOA(8178, 8388602, F81, 2, 14) (dual of [(8388602, 2), 16777126, 15]-NRT-code), using (u, u+v)-construction based on
- linear OOA(8125, 4194301, F81, 2, 7) (dual of [(4194301, 2), 8388577, 8]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8125, 8388602, F81, 7) (dual of [8388602, 8388577, 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 2-folding [i] based on linear OA(8125, 8388602, F81, 7) (dual of [8388602, 8388577, 8]-code), using
- 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
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(8180, large, F81, 2, 14) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(8182, large, F81, 2, 14) | [i] | ||
| 3 | Linear OOA(8179, 8388602, F81, 2, 14) (dual of [(8388602, 2), 16777125, 15]-NRT-code) | [i] | OOA Duplication | |
| 4 | Linear OOA(8178, 4194301, F81, 3, 14) (dual of [(4194301, 3), 12582825, 15]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(8178, 4194301, F81, 4, 14) (dual of [(4194301, 4), 16777126, 15]-NRT-code) | [i] | ||
| 6 | Linear OOA(8178, 2097150, F81, 18, 14) (dual of [(2097150, 18), 37748622, 15]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |