Information on Result #691817
Linear OA(1675, 65550, F16, 20) (dual of [65550, 65475, 21]-code), using construction X applied to Ce(19) ⊂ Ce(16) based on
- linear OA(1673, 65536, F16, 20) (dual of [65536, 65463, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(1661, 65536, F16, 17) (dual of [65536, 65475, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(162, 14, F16, 2) (dual of [14, 12, 3]-code or 14-arc in PG(1,16)), using
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- Reed–Solomon code RS(14,16) [i]
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), 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(1676, 65551, F16, 20) (dual of [65551, 65475, 21]-code) | [i] | Code Embedding in Larger Space | |
| 2 | OA(8100, 65550, S8, 20) | [i] | Discarding Parts of the Base for OAs | |
| 3 | Linear OOA(1675, 44897, F16, 2, 20) (dual of [(44897, 2), 89719, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Digital (55, 75, 44897)-net over F16 | [i] | ||
| 5 | Linear OOA(1675, 32775, F16, 2, 20) (dual of [(32775, 2), 65475, 21]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(1675, 6555, F16, 20, 20) (dual of [(6555, 20), 131025, 21]-NRT-code) | [i] | OA Folding and Stacking | |