Information on Result #731307
Linear OA(8164, 8204, F8, 41) (dual of [8204, 8040, 42]-code), using trace code based on linear OA(6482, 4102, F64, 41) (dual of [4102, 4020, 42]-code), using
- construction X applied to C([0,20]) ⊂ C([0,19]) [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(6477, 4097, F64, 39) (dual of [4097, 4020, 40]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,19], and minimum distance d ≥ |{−19,−18,…,19}|+1 = 40 (BCH-bound) [i]
- linear OA(641, 5, F64, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(8165, 8205, F8, 41) (dual of [8205, 8040, 42]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(8164, 4102, F8, 2, 41) (dual of [(4102, 2), 8040, 42]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(8164, 2734, F8, 3, 41) (dual of [(2734, 3), 8038, 42]-NRT-code) | [i] | ||