Information on Result #731606
Linear OA(1682, 131088, F16, 20) (dual of [131088, 131006, 21]-code), using trace code based on linear OA(25641, 65544, F256, 20) (dual of [65544, 65503, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(16) [i] based on
- linear OA(25639, 65536, F256, 20) (dual of [65536, 65497, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(25633, 65536, F256, 17) (dual of [65536, 65503, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(2562, 8, F256, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,256)), using
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- Reed–Solomon code RS(254,256) [i]
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), 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(1683, 131089, F16, 20) (dual of [131089, 131006, 21]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(1682, 131088, F16, 2, 20) (dual of [(131088, 2), 262094, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (62, 82, 131088)-net over F16 | [i] | ||
| 4 | Linear OA(1683, 131090, F16, 20) (dual of [131090, 131007, 21]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OOA(1682, 65544, F16, 2, 20) (dual of [(65544, 2), 131006, 21]-NRT-code) | [i] | OOA Folding | |