Information on Result #1315039
Linear OA(27101, 866, F27, 48) (dual of [866, 765, 49]-code), using 125 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 0, 0, 0, 1, 9 times 0, 1, 20 times 0, 1, 36 times 0, 1, 50 times 0) based on linear OA(2792, 732, F27, 48) (dual of [732, 640, 49]-code), using
- construction XX applied to C1 = C([727,45]), C2 = C([0,46]), C3 = C1 + C2 = C([0,45]), and C∩ = C1 ∩ C2 = C([727,46]) [i] based on
- linear OA(2790, 728, F27, 47) (dual of [728, 638, 48]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,45}, and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(2790, 728, F27, 47) (dual of [728, 638, 48]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,46], and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(2792, 728, F27, 48) (dual of [728, 636, 49]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,46}, and designed minimum distance d ≥ |I|+1 = 49 [i]
- linear OA(2788, 728, F27, 46) (dual of [728, 640, 47]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,45], and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(270, 2, F27, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(270, 2, F27, 0) (dual of [2, 2, 1]-code) (see above)
Mode: Linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n 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(27101, 866, F27, 2, 48) (dual of [(866, 2), 1631, 49]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (53, 101, 866)-net over F27 | [i] | ||
| 3 | Linear OOA(27101, 433, F27, 2, 48) (dual of [(433, 2), 765, 49]-NRT-code) | [i] | OOA Folding | |