Information on Result #725913
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]) 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 OA(2744, 760, F27, 18) (dual of [760, 716, 19]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(2745, 770, F27, 18) (dual of [770, 725, 19]-code) | [i] | ||
| 3 | Linear OA(2746, 780, F27, 18) (dual of [780, 734, 19]-code) | [i] | ||
| 4 | Linear OA(2747, 784, F27, 18) (dual of [784, 737, 19]-code) | [i] | ||
| 5 | Linear OA(2748, 796, F27, 18) (dual of [796, 748, 19]-code) | [i] | ||
| 6 | Linear OA(2749, 800, F27, 18) (dual of [800, 751, 19]-code) | [i] | ||
| 7 | Linear OA(2750, 838, F27, 18) (dual of [838, 788, 19]-code) | [i] | ||
| 8 | Linear OA(2739, 747, F27, 18) (dual of [747, 708, 19]-code) | [i] | Varšamov–Edel Lengthening | |
| 9 | Linear OA(2740, 773, F27, 18) (dual of [773, 733, 19]-code) | [i] | ||
| 10 | Linear OA(2741, 838, F27, 18) (dual of [838, 797, 19]-code) | [i] | ||
| 11 | Linear OA(2742, 968, F27, 18) (dual of [968, 926, 19]-code) | [i] | ||
| 12 | Linear OA(2743, 1162, F27, 18) (dual of [1162, 1119, 19]-code) | [i] | ||
| 13 | Linear OOA(2735, 366, F27, 2, 18) (dual of [(366, 2), 697, 19]-NRT-code) | [i] | OOA Folding | |