Information on Result #676682
Linear OA(3116, 754, F3, 28) (dual of [754, 638, 29]-code), using construction X applied to Ce(27) ⊂ Ce(22) based on
- 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(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(37, 25, F3, 4) (dual of [25, 18, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(37, 26, F3, 4) (dual of [26, 19, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 26 = 33−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(37, 26, F3, 4) (dual of [26, 19, 5]-code), 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 OOA(3116, 657, F3, 2, 28) (dual of [(657, 2), 1198, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3116, 657, F3, 3, 28) (dual of [(657, 3), 1855, 29]-NRT-code) | [i] | ||
| 3 | Linear OOA(3116, 657, F3, 4, 28) (dual of [(657, 4), 2512, 29]-NRT-code) | [i] | ||
| 4 | Linear OOA(3116, 657, F3, 5, 28) (dual of [(657, 5), 3169, 29]-NRT-code) | [i] | ||
| 5 | Digital (88, 116, 657)-net over F3 | [i] | ||