Information on Result #865319
Linear OOA(2731, 366, F27, 2, 16) (dual of [(366, 2), 701, 17]-NRT-code), using OOA 2-folding based on linear OA(2731, 732, F27, 16) (dual of [732, 701, 17]-code), using
- construction XX applied to C1 = C([727,13]), C2 = C([0,14]), C3 = C1 + C2 = C([0,13]), and C∩ = C1 ∩ C2 = C([727,14]) [i] based on
- linear OA(2729, 728, F27, 15) (dual of [728, 699, 16]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,13}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(2729, 728, F27, 15) (dual of [728, 699, 16]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(2731, 728, F27, 16) (dual of [728, 697, 17]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,14}, and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(2727, 728, F27, 14) (dual of [728, 701, 15]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [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: Constructive and 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(2739, 394, F27, 2, 16) (dual of [(394, 2), 749, 17]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(2740, 404, F27, 2, 16) (dual of [(404, 2), 768, 17]-NRT-code) | [i] | ||
| 3 | Linear OOA(2741, 414, F27, 2, 16) (dual of [(414, 2), 787, 17]-NRT-code) | [i] | ||
| 4 | Linear OOA(2742, 418, F27, 2, 16) (dual of [(418, 2), 794, 17]-NRT-code) | [i] | ||
| 5 | Linear OOA(2743, 430, F27, 2, 16) (dual of [(430, 2), 817, 17]-NRT-code) | [i] | ||
| 6 | Linear OOA(2744, 434, F27, 2, 16) (dual of [(434, 2), 824, 17]-NRT-code) | [i] | ||
| 7 | Digital (15, 31, 334)-net over F27 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |