Information on Result #1314778
Linear OA(2741, 1227, F27, 17) (dual of [1227, 1186, 18]-code), using 487 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 1, 9 times 0, 1, 30 times 0, 1, 75 times 0, 1, 148 times 0, 1, 217 times 0) based on linear OA(2733, 732, F27, 17) (dual of [732, 699, 18]-code), using
- construction XX applied to C1 = C([727,14]), C2 = C([0,15]), C3 = C1 + C2 = C([0,14]), and C∩ = C1 ∩ C2 = C([727,15]) [i] based on
- 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(2731, 728, F27, 16) (dual of [728, 697, 17]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(2733, 728, F27, 17) (dual of [728, 695, 18]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,15}, and designed minimum distance d ≥ |I|+1 = 18 [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(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(2741, 1227, F27, 2, 17) (dual of [(1227, 2), 2413, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (24, 41, 1227)-net over F27 | [i] | ||
| 3 | Linear OOA(2741, 613, F27, 2, 17) (dual of [(613, 2), 1185, 18]-NRT-code) | [i] | OOA Folding | |