Information on Result #731237
Linear OA(8132, 8204, F8, 33) (dual of [8204, 8072, 34]-code), using trace code based on linear OA(6466, 4102, F64, 33) (dual of [4102, 4036, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,15]) [i] based on
- linear OA(6465, 4097, F64, 33) (dual of [4097, 4032, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(6461, 4097, F64, 31) (dual of [4097, 4036, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (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(8133, 8205, F8, 33) (dual of [8205, 8072, 34]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(8132, 4102, F8, 2, 33) (dual of [(4102, 2), 8072, 34]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(8132, 2734, F8, 3, 33) (dual of [(2734, 3), 8070, 34]-NRT-code) | [i] | ||