Information on Result #677494
Linear OA(323, 251, F3, 7) (dual of [251, 228, 8]-code), using construction XX applied to Ce(6) ⊂ Ce(4) ⊂ Ce(3) based on
- 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(311, 243, F3, 4) (dual of [243, 232, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(31, 7, F3, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [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(323, 160, F3, 2, 7) (dual of [(160, 2), 297, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(323, 160, F3, 3, 7) (dual of [(160, 3), 457, 8]-NRT-code) | [i] | ||
| 3 | Linear OOA(323, 160, F3, 4, 7) (dual of [(160, 4), 617, 8]-NRT-code) | [i] | ||
| 4 | Linear OOA(323, 160, F3, 5, 7) (dual of [(160, 5), 777, 8]-NRT-code) | [i] | ||
| 5 | Digital (16, 23, 160)-net over F3 | [i] | ||