Information on Result #1831768
OOA(27101, 4197582, S27, 2, 17), using (u, u+v)-construction based on
- OOA(2720, 3281, S27, 2, 8), using
- OOA 2-folding [i] based on OA(2720, 6562, S27, 8), using
- discarding factors based on OA(2720, 6563, S27, 8), using
- discarding parts of the base [i] based on linear OA(8115, 6563, F81, 8) (dual of [6563, 6548, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(8115, 6561, F81, 8) (dual of [6561, 6546, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(8113, 6561, F81, 7) (dual of [6561, 6548, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(810, 2, F81, 0) (dual of [2, 2, 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(7) ⊂ Ce(6) [i] based on
- discarding parts of the base [i] based on linear OA(8115, 6563, F81, 8) (dual of [6563, 6548, 9]-code), using
- discarding factors based on OA(2720, 6563, S27, 8), using
- OOA 2-folding [i] based on OA(2720, 6562, S27, 8), using
- linear OOA(2781, 4194301, F27, 2, 17) (dual of [(4194301, 2), 8388521, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2781, 8388602, F27, 17) (dual of [8388602, 8388521, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2781, large, F27, 17) (dual of [large, large−81, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 2710−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2781, large, F27, 17) (dual of [large, large−81, 18]-code), using
- OOA 2-folding [i] based on linear OA(2781, 8388602, F27, 17) (dual of [8388602, 8388521, 18]-code), using
Mode: Constructive.
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 | OOA(27101, 1049395, S27, 18, 17) | [i] | OOA Folding and Stacking with Additional Row | |