Information on Result #1831723
OOA(2776, 4197582, S27, 2, 13), using (u, u+v)-construction based on
- OOA(2715, 3281, S27, 2, 6), using
- OOA 2-folding [i] based on OA(2715, 6562, S27, 6), using
- discarding factors based on OA(2715, 6563, S27, 6), using
- discarding parts of the base [i] based on linear OA(8111, 6563, F81, 6) (dual of [6563, 6552, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(8111, 6561, F81, 6) (dual of [6561, 6550, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(819, 6561, F81, 5) (dual of [6561, 6552, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [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(5) ⊂ Ce(4) [i] based on
- discarding parts of the base [i] based on linear OA(8111, 6563, F81, 6) (dual of [6563, 6552, 7]-code), using
- discarding factors based on OA(2715, 6563, S27, 6), using
- OOA 2-folding [i] based on OA(2715, 6562, S27, 6), using
- linear OOA(2761, 4194301, F27, 2, 13) (dual of [(4194301, 2), 8388541, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2761, 8388602, F27, 13) (dual of [8388602, 8388541, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(2761, large, F27, 13) (dual of [large, large−61, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 2710−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2761, large, F27, 13) (dual of [large, large−61, 14]-code), using
- OOA 2-folding [i] based on linear OA(2761, 8388602, F27, 13) (dual of [8388602, 8388541, 14]-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(2776, 1399193, S27, 14, 13) | [i] | OOA Folding and Stacking with Additional Row | |