Information on Result #675401
Linear OA(3249, 6634, F3, 43) (dual of [6634, 6385, 44]-code), using construction X applied to C([0,21]) ⊂ C([0,16]) based on
- linear OA(3225, 6562, F3, 43) (dual of [6562, 6337, 44]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,21], and minimum distance d ≥ |{−21,−20,…,21}|+1 = 44 (BCH-bound) [i]
- linear OA(3177, 6562, F3, 33) (dual of [6562, 6385, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(324, 72, F3, 9) (dual of [72, 48, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(324, 80, F3, 9) (dual of [80, 56, 10]-code), using
- the primitive narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
- discarding factors / shortening the dual code based on linear OA(324, 80, F3, 9) (dual of [80, 56, 10]-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 OA(3248, 6633, F3, 42) (dual of [6633, 6385, 43]-code) | [i] | Truncation | |
| 2 | Linear OOA(3249, 6168, F3, 2, 43) (dual of [(6168, 2), 12087, 44]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(3249, 6168, F3, 3, 43) (dual of [(6168, 3), 18255, 44]-NRT-code) | [i] | ||
| 4 | Linear OOA(3249, 6168, F3, 4, 43) (dual of [(6168, 4), 24423, 44]-NRT-code) | [i] | ||
| 5 | Linear OOA(3249, 6168, F3, 5, 43) (dual of [(6168, 5), 30591, 44]-NRT-code) | [i] | ||
| 6 | Digital (206, 249, 6168)-net over F3 | [i] | ||
| 7 | Linear OOA(3249, 3317, F3, 2, 43) (dual of [(3317, 2), 6385, 44]-NRT-code) | [i] | OOA Folding | |