Information on Result #1315031
Linear OA(2799, 858, F27, 47) (dual of [858, 759, 48]-code), using 117 step Varšamov–Edel lengthening with (ri) = (4, 1, 0, 0, 0, 1, 7 times 0, 1, 18 times 0, 1, 34 times 0, 1, 49 times 0) based on linear OA(2790, 732, F27, 47) (dual of [732, 642, 48]-code), using
- construction XX applied to C1 = C([727,44]), C2 = C([0,45]), C3 = C1 + C2 = C([0,44]), and C∩ = C1 ∩ C2 = C([727,45]) [i] based on
- linear OA(2788, 728, F27, 46) (dual of [728, 640, 47]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,44}, and designed minimum distance d ≥ |I|+1 = 47 [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(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(2786, 728, F27, 45) (dual of [728, 642, 46]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,44], and designed minimum distance d ≥ |I|+1 = 46 [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(2799, 858, F27, 2, 47) (dual of [(858, 2), 1617, 48]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (52, 99, 858)-net over F27 | [i] | ||
| 3 | Linear OOA(2799, 429, F27, 2, 47) (dual of [(429, 2), 759, 48]-NRT-code) | [i] | OOA Folding | |