Information on Result #900636
Linear OOA(2797, 8388602, F27, 2, 14) (dual of [(8388602, 2), 16777107, 15]-NRT-code), using (u, u+v)-construction based on
- linear OOA(2731, 4194301, F27, 2, 7) (dual of [(4194301, 2), 8388571, 8]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2731, 8388602, F27, 7) (dual of [8388602, 8388571, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(2731, large, F27, 7) (dual of [large, large−31, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 2710−1, 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(2731, large, F27, 7) (dual of [large, large−31, 8]-code), using
- OOA 2-folding [i] based on linear OA(2731, 8388602, F27, 7) (dual of [8388602, 8388571, 8]-code), using
- linear OOA(2766, 4194301, F27, 2, 14) (dual of [(4194301, 2), 8388536, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2766, 8388602, F27, 14) (dual of [8388602, 8388536, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(2766, large, F27, 14) (dual of [large, large−66, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 275−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(2766, large, F27, 14) (dual of [large, large−66, 15]-code), using
- OOA 2-folding [i] based on linear OA(2766, 8388602, F27, 14) (dual of [8388602, 8388536, 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(2799, large, F27, 2, 14) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(27101, large, F27, 2, 14) | [i] | ||
| 3 | Linear OOA(27103, large, F27, 2, 14) | [i] | ||
| 4 | Linear OOA(27105, large, F27, 2, 14) | [i] | ||
| 5 | Linear OOA(27107, large, F27, 2, 14) | [i] | ||
| 6 | Linear OOA(27109, large, F27, 2, 14) | [i] | ||
| 7 | Linear OOA(2798, 8388602, F27, 2, 14) (dual of [(8388602, 2), 16777106, 15]-NRT-code) | [i] | OOA Duplication | |
| 8 | Linear OOA(2797, 2097150, F27, 18, 14) (dual of [(2097150, 18), 37748603, 15]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |