Information on Result #1314916
Linear OA(2774, 853, F27, 34) (dual of [853, 779, 35]-code), using 111 step Varšamov–Edel lengthening with (ri) = (5, 0, 1, 0, 0, 0, 1, 7 times 0, 1, 16 times 0, 1, 29 times 0, 1, 49 times 0) based on linear OA(2764, 732, F27, 34) (dual of [732, 668, 35]-code), using
- construction XX applied to C1 = C([727,31]), C2 = C([0,32]), C3 = C1 + C2 = C([0,31]), and C∩ = C1 ∩ C2 = C([727,32]) [i] based on
- linear OA(2762, 728, F27, 33) (dual of [728, 666, 34]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,31}, and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(2762, 728, F27, 33) (dual of [728, 666, 34]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,32], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(2764, 728, F27, 34) (dual of [728, 664, 35]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,32}, and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(2760, 728, F27, 32) (dual of [728, 668, 33]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,31], and designed minimum distance d ≥ |I|+1 = 33 [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(2774, 853, F27, 2, 34) (dual of [(853, 2), 1632, 35]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (40, 74, 853)-net over F27 | [i] | ||
| 3 | Linear OOA(2774, 426, F27, 2, 34) (dual of [(426, 2), 778, 35]-NRT-code) | [i] | OOA Folding | |