Information on Result #677001
Linear OA(3126, 738, F3, 32) (dual of [738, 612, 33]-code), using construction XX applied to Ce(31) ⊂ Ce(30) ⊂ Ce(28) based on
- linear OA(3124, 729, F3, 32) (dual of [729, 605, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(3118, 729, F3, 31) (dual of [729, 611, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- 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(30, 7, F3, 0) (dual of [7, 7, 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(3126, 560, F3, 2, 32) (dual of [(560, 2), 994, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3126, 560, F3, 3, 32) (dual of [(560, 3), 1554, 33]-NRT-code) | [i] | ||
| 3 | Linear OOA(3126, 560, F3, 4, 32) (dual of [(560, 4), 2114, 33]-NRT-code) | [i] | ||
| 4 | Linear OOA(3126, 560, F3, 5, 32) (dual of [(560, 5), 2674, 33]-NRT-code) | [i] | ||
| 5 | Digital (94, 126, 560)-net over F3 | [i] | ||