Information on Result #677028
Linear OA(393, 738, F3, 23) (dual of [738, 645, 24]-code), using construction XX applied to Ce(22) ⊂ Ce(21) ⊂ Ce(19) based on
- linear OA(391, 729, F3, 23) (dual of [729, 638, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(385, 729, F3, 22) (dual of [729, 644, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(379, 729, F3, 20) (dual of [729, 650, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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(393, 516, F3, 2, 23) (dual of [(516, 2), 939, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(393, 516, F3, 3, 23) (dual of [(516, 3), 1455, 24]-NRT-code) | [i] | ||
| 3 | Linear OOA(393, 516, F3, 4, 23) (dual of [(516, 4), 1971, 24]-NRT-code) | [i] | ||
| 4 | Linear OOA(393, 516, F3, 5, 23) (dual of [(516, 5), 2487, 24]-NRT-code) | [i] | ||
| 5 | Digital (70, 93, 516)-net over F3 | [i] | ||