Information on Result #677016
Linear OA(3114, 735, F3, 29) (dual of [735, 621, 30]-code), using construction XX applied to Ce(28) ⊂ Ce(27) ⊂ Ce(25) based on
- linear OA(3112, 729, F3, 29) (dual of [729, 617, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(3109, 729, F3, 28) (dual of [729, 620, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(3103, 729, F3, 26) (dual of [729, 626, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(30, 4, F3, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(31, 2, F3, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
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(3114, 519, F3, 2, 29) (dual of [(519, 2), 924, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3114, 519, F3, 3, 29) (dual of [(519, 3), 1443, 30]-NRT-code) | [i] | ||
| 3 | Linear OOA(3114, 519, F3, 4, 29) (dual of [(519, 4), 1962, 30]-NRT-code) | [i] | ||
| 4 | Linear OOA(3114, 519, F3, 5, 29) (dual of [(519, 5), 2481, 30]-NRT-code) | [i] | ||
| 5 | Digital (85, 114, 519)-net over F3 | [i] | ||
| 6 | Linear OOA(3114, 245, F3, 3, 29) (dual of [(245, 3), 621, 30]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3114, 147, F3, 5, 29) (dual of [(147, 5), 621, 30]-NRT-code) | [i] | ||