Information on Result #676528
Linear OA(3112, 732, F3, 29) (dual of [732, 620, 30]-code), using construction X applied to Ce(28) ⊂ Ce(27) 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(30, 3, F3, 0) (dual of [3, 3, 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
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(3113, 733, F3, 29) (dual of [733, 620, 30]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3122, 763, F3, 29) (dual of [763, 641, 30]-code) | [i] | Varšamov–Edel Lengthening | |
| 3 | Linear OA(3123, 774, F3, 29) (dual of [774, 651, 30]-code) | [i] | ||
| 4 | Linear OA(3124, 788, F3, 29) (dual of [788, 664, 30]-code) | [i] | ||
| 5 | Linear OA(3125, 805, F3, 29) (dual of [805, 680, 30]-code) | [i] | ||
| 6 | Linear OA(3126, 826, F3, 29) (dual of [826, 700, 30]-code) | [i] | ||
| 7 | Linear OA(3127, 851, F3, 29) (dual of [851, 724, 30]-code) | [i] | ||
| 8 | Linear OA(3128, 879, F3, 29) (dual of [879, 751, 30]-code) | [i] | ||
| 9 | Linear OA(3129, 910, F3, 29) (dual of [910, 781, 30]-code) | [i] | ||
| 10 | Linear OA(3130, 943, F3, 29) (dual of [943, 813, 30]-code) | [i] | ||
| 11 | Linear OA(3131, 979, F3, 29) (dual of [979, 848, 30]-code) | [i] | ||
| 12 | Linear OOA(3112, 366, F3, 2, 29) (dual of [(366, 2), 620, 30]-NRT-code) | [i] | OOA Folding | |
| 13 | Linear OOA(3112, 244, F3, 3, 29) (dual of [(244, 3), 620, 30]-NRT-code) | [i] | ||
| 14 | Linear OOA(3112, 183, F3, 4, 29) (dual of [(183, 4), 620, 30]-NRT-code) | [i] | ||
| 15 | Linear OOA(3112, 146, F3, 5, 29) (dual of [(146, 5), 618, 30]-NRT-code) | [i] | ||