Information on Result #677031
Linear OA(391, 748, F3, 22) (dual of [748, 657, 23]-code), using construction XX applied to Ce(21) ⊂ Ce(18) ⊂ Ce(16) based on
- 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(373, 729, F3, 19) (dual of [729, 656, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(367, 729, F3, 17) (dual of [729, 662, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(34, 17, F3, 2) (dual of [17, 13, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), 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(391, 565, F3, 2, 22) (dual of [(565, 2), 1039, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(391, 565, F3, 3, 22) (dual of [(565, 3), 1604, 23]-NRT-code) | [i] | ||
| 3 | Linear OOA(391, 565, F3, 4, 22) (dual of [(565, 4), 2169, 23]-NRT-code) | [i] | ||
| 4 | Linear OOA(391, 565, F3, 5, 22) (dual of [(565, 5), 2734, 23]-NRT-code) | [i] | ||
| 5 | Digital (69, 91, 565)-net over F3 | [i] | ||