Information on Result #699360
Linear OA(8176, 6597, F81, 33) (dual of [6597, 6521, 34]-code), using construction X applied to C([0,16]) ⊂ C([0,10]) based on
- linear OA(8165, 6562, F81, 33) (dual of [6562, 6497, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(8141, 6562, F81, 21) (dual of [6562, 6521, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(8111, 35, F81, 11) (dual of [35, 24, 12]-code or 35-arc in PG(10,81)), using
- discarding factors / shortening the dual code based on linear OA(8111, 81, F81, 11) (dual of [81, 70, 12]-code or 81-arc in PG(10,81)), using
- Reed–Solomon code RS(70,81) [i]
- discarding factors / shortening the dual code based on linear OA(8111, 81, F81, 11) (dual of [81, 70, 12]-code or 81-arc in PG(10,81)), 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(8176, 6416, F81, 2, 33) (dual of [(6416, 2), 12756, 34]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8176, 6416, F81, 3, 33) (dual of [(6416, 3), 19172, 34]-NRT-code) | [i] | ||
| 3 | Linear OOA(8176, 6416, F81, 4, 33) (dual of [(6416, 4), 25588, 34]-NRT-code) | [i] | ||
| 4 | Digital (43, 76, 6416)-net over F81 | [i] | ||
| 5 | Linear OOA(8176, 3298, F81, 2, 33) (dual of [(3298, 2), 6520, 34]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8176, 2199, F81, 3, 33) (dual of [(2199, 3), 6521, 34]-NRT-code) | [i] | ||
| 7 | Linear OOA(8176, 1649, F81, 4, 33) (dual of [(1649, 4), 6520, 34]-NRT-code) | [i] | ||