Information on Result #900768
Linear OOA(27106, 4204150, F27, 2, 17) (dual of [(4204150, 2), 8408194, 18]-NRT-code), using (u, u+v)-construction based on
- linear OOA(2725, 9849, F27, 2, 8) (dual of [(9849, 2), 19673, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2725, 19698, F27, 8) (dual of [19698, 19673, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(3) [i] based on
- linear OA(2722, 19683, F27, 8) (dual of [19683, 19661, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- 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(273, 15, F27, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,27) or 15-cap in PG(2,27)), using
- discarding factors / shortening the dual code based on linear OA(273, 27, F27, 3) (dual of [27, 24, 4]-code or 27-arc in PG(2,27) or 27-cap in PG(2,27)), using
- Reed–Solomon code RS(24,27) [i]
- discarding factors / shortening the dual code based on linear OA(273, 27, F27, 3) (dual of [27, 24, 4]-code or 27-arc in PG(2,27) or 27-cap in PG(2,27)), using
- construction X applied to Ce(7) ⊂ Ce(3) [i] based on
- OOA 2-folding [i] based on linear OA(2725, 19698, F27, 8) (dual of [19698, 19673, 9]-code), 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 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(27106, 1051037, F27, 18, 17) (dual of [(1051037, 18), 18918560, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |