Information on Result #675513
Linear OA(3231, 6591, F3, 42) (dual of [6591, 6360, 43]-code), using construction X applied to Ce(42) ⊂ Ce(37) based on
- linear OA(3225, 6561, F3, 43) (dual of [6561, 6336, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(3201, 6561, F3, 38) (dual of [6561, 6360, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(36, 30, F3, 3) (dual of [30, 24, 4]-code or 30-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), 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(3231, 4329, F3, 2, 42) (dual of [(4329, 2), 8427, 43]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3231, 4329, F3, 3, 42) (dual of [(4329, 3), 12756, 43]-NRT-code) | [i] | ||
| 3 | Linear OOA(3231, 4329, F3, 4, 42) (dual of [(4329, 4), 17085, 43]-NRT-code) | [i] | ||
| 4 | Linear OOA(3231, 4329, F3, 5, 42) (dual of [(4329, 5), 21414, 43]-NRT-code) | [i] | ||
| 5 | Digital (189, 231, 4329)-net over F3 | [i] | ||
| 6 | Linear OOA(3231, 3295, F3, 2, 42) (dual of [(3295, 2), 6359, 43]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3231, 2197, F3, 3, 42) (dual of [(2197, 3), 6360, 43]-NRT-code) | [i] | ||
| 8 | Linear OOA(3231, 1647, F3, 4, 42) (dual of [(1647, 4), 6357, 43]-NRT-code) | [i] | ||
| 9 | Linear OOA(3231, 1318, F3, 5, 42) (dual of [(1318, 5), 6359, 43]-NRT-code) | [i] | ||