Information on Result #865439
Linear OOA(2735, 366, F27, 2, 18) (dual of [(366, 2), 697, 19]-NRT-code), using OOA 2-folding based on linear OA(2735, 732, F27, 18) (dual of [732, 697, 19]-code), using
- construction XX applied to C1 = C([727,15]), C2 = C([0,16]), C3 = C1 + C2 = C([0,15]), and C∩ = C1 ∩ C2 = C([727,16]) [i] based on
- 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(2733, 728, F27, 17) (dual of [728, 695, 18]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(2735, 728, F27, 18) (dual of [728, 693, 19]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,16}, and designed minimum distance d ≥ |I|+1 = 19 [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(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(2744, 394, F27, 2, 18) (dual of [(394, 2), 744, 19]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(2745, 404, F27, 2, 18) (dual of [(404, 2), 763, 19]-NRT-code) | [i] | ||
| 3 | Linear OOA(2746, 414, F27, 2, 18) (dual of [(414, 2), 782, 19]-NRT-code) | [i] | ||
| 4 | Linear OOA(2747, 418, F27, 2, 18) (dual of [(418, 2), 789, 19]-NRT-code) | [i] | ||
| 5 | Linear OOA(2748, 430, F27, 2, 18) (dual of [(430, 2), 812, 19]-NRT-code) | [i] | ||
| 6 | Linear OOA(2749, 434, F27, 2, 18) (dual of [(434, 2), 819, 19]-NRT-code) | [i] | ||
| 7 | Linear OOA(2750, 442, F27, 2, 18) (dual of [(442, 2), 834, 19]-NRT-code) | [i] | ||
| 8 | Digital (17, 35, 341)-net over F27 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |