Information on Result #677493
Linear OA(328, 251, F3, 8) (dual of [251, 223, 9]-code), using construction XX applied to Ce(7) ⊂ Ce(6) ⊂ Ce(4) based on
- linear OA(326, 243, F3, 8) (dual of [243, 217, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(321, 243, F3, 7) (dual of [243, 222, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(316, 243, F3, 5) (dual of [243, 227, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(30, 6, F3, 0) (dual of [6, 6, 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(328, 205, F3, 2, 8) (dual of [(205, 2), 382, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(328, 205, F3, 3, 8) (dual of [(205, 3), 587, 9]-NRT-code) | [i] | ||
| 3 | Linear OOA(328, 205, F3, 4, 8) (dual of [(205, 4), 792, 9]-NRT-code) | [i] | ||
| 4 | Linear OOA(328, 205, F3, 5, 8) (dual of [(205, 5), 997, 9]-NRT-code) | [i] | ||
| 5 | Digital (20, 28, 205)-net over F3 | [i] | ||