Information on Result #900462
Linear OOA(2752, 4204146, F27, 2, 9) (dual of [(4204146, 2), 8408240, 10]-NRT-code), using (u, u+v)-construction based on
- linear OOA(2711, 9845, F27, 2, 4) (dual of [(9845, 2), 19679, 5]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2711, 19690, F27, 4) (dual of [19690, 19679, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(1) [i] based on
- linear OA(2710, 19683, F27, 4) (dual of [19683, 19673, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(274, 19683, F27, 2) (dual of [19683, 19679, 3]-code), using an extension Ce(1) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,1], and designed minimum distance d ≥ |I|+1 = 2 [i]
- linear OA(271, 7, F27, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(271, s, F27, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(3) ⊂ Ce(1) [i] based on
- OOA 2-folding [i] based on linear OA(2711, 19690, F27, 4) (dual of [19690, 19679, 5]-code), using
- linear OOA(2741, 4194301, F27, 2, 9) (dual of [(4194301, 2), 8388561, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2741, 8388602, F27, 9) (dual of [8388602, 8388561, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(2741, large, F27, 9) (dual of [large, large−41, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 2710−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2741, large, F27, 9) (dual of [large, large−41, 10]-code), using
- OOA 2-folding [i] based on linear OA(2741, 8388602, F27, 9) (dual of [8388602, 8388561, 10]-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(2752, 2102072, F27, 10, 9) (dual of [(2102072, 10), 21020668, 10]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |