Information on Result #2281031
Linear OA(868, 4108, F8, 19) (dual of [4108, 4040, 20]-code), using 2 times code embedding in larger space based on linear OA(866, 4106, F8, 19) (dual of [4106, 4040, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
- linear OA(865, 4097, F8, 19) (dual of [4097, 4032, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 88−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(857, 4097, F8, 17) (dual of [4097, 4040, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 88−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(81, 9, F8, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 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 OOA(868, 3706, F8, 2, 19) (dual of [(3706, 2), 7344, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(868, 3706, F8, 3, 19) (dual of [(3706, 3), 11050, 20]-NRT-code) | [i] | ||
| 3 | Digital (49, 68, 3706)-net over F8 | [i] | ||