Information on Result #677005
Linear OA(3120, 738, F3, 31) (dual of [738, 618, 32]-code), using construction XX applied to Ce(30) ⊂ Ce(28) ⊂ Ce(27) based on
- 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(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(31, 8, F3, 1) (dual of [8, 7, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [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(3120, 505, F3, 2, 31) (dual of [(505, 2), 890, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3120, 505, F3, 3, 31) (dual of [(505, 3), 1395, 32]-NRT-code) | [i] | ||
| 3 | Linear OOA(3120, 505, F3, 4, 31) (dual of [(505, 4), 1900, 32]-NRT-code) | [i] | ||
| 4 | Linear OOA(3120, 505, F3, 5, 31) (dual of [(505, 5), 2405, 32]-NRT-code) | [i] | ||
| 5 | Digital (89, 120, 505)-net over F3 | [i] | ||
| 6 | Linear OOA(3120, 369, F3, 2, 31) (dual of [(369, 2), 618, 32]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3120, 246, F3, 3, 31) (dual of [(246, 3), 618, 32]-NRT-code) | [i] | ||