Information on Result #731316
Linear OA(8168, 8216, F8, 41) (dual of [8216, 8048, 42]-code), using trace code based on linear OA(6484, 4108, F64, 41) (dual of [4108, 4024, 42]-code), using
- construction X applied to C([0,20]) ⊂ C([0,18]) [i] based on
- linear OA(6481, 4097, F64, 41) (dual of [4097, 4016, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
- linear OA(6473, 4097, F64, 37) (dual of [4097, 4024, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(643, 11, F64, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,64) or 11-cap in PG(2,64)), using
- discarding factors / shortening the dual code based on linear OA(643, 64, F64, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
- Reed–Solomon code RS(61,64) [i]
- discarding factors / shortening the dual code based on linear OA(643, 64, F64, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), 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(8169, 8217, F8, 41) (dual of [8217, 8048, 42]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(8168, 4108, F8, 2, 41) (dual of [(4108, 2), 8048, 42]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(8168, 2738, F8, 3, 41) (dual of [(2738, 3), 8046, 42]-NRT-code) | [i] | ||