Information on Result #731631
Linear OA(1698, 131112, F16, 22) (dual of [131112, 131014, 23]-code), using trace code based on linear OA(25649, 65556, F256, 22) (dual of [65556, 65507, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(14) [i] based on
- linear OA(25643, 65536, F256, 22) (dual of [65536, 65493, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(25629, 65536, F256, 15) (dual of [65536, 65507, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(2566, 20, F256, 6) (dual of [20, 14, 7]-code or 20-arc in PG(5,256)), using
- discarding factors / shortening the dual code based on linear OA(2566, 256, F256, 6) (dual of [256, 250, 7]-code or 256-arc in PG(5,256)), using
- Reed–Solomon code RS(250,256) [i]
- discarding factors / shortening the dual code based on linear OA(2566, 256, F256, 6) (dual of [256, 250, 7]-code or 256-arc in PG(5,256)), 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(1699, 131113, F16, 22) (dual of [131113, 131014, 23]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(1698, 65556, F16, 2, 22) (dual of [(65556, 2), 131014, 23]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(1698, 11919, F16, 22, 22) (dual of [(11919, 22), 262120, 23]-NRT-code) | [i] | OA Folding and Stacking | |