Information on Result #734928
Linear OA(6454, 4163, F64, 22) (dual of [4163, 4109, 23]-code), using (u, u+v)-construction based on
- linear OA(6411, 65, F64, 11) (dual of [65, 54, 12]-code or 65-arc in PG(10,64)), using
- extended Reed–Solomon code RSe(54,64) [i]
- the expurgated narrow-sense BCH-code C(I) with length 65 | 642−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(6443, 4098, F64, 22) (dual of [4098, 4055, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- linear OA(6443, 4096, F64, 22) (dual of [4096, 4053, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(6441, 4096, F64, 21) (dual of [4096, 4055, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(640, 2, F64, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
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(6454, 2081, F64, 2, 22) (dual of [(2081, 2), 4108, 23]-NRT-code) | [i] | OOA Folding | |