Information on Result #681271
Linear OA(458, 266, F4, 19) (dual of [266, 208, 20]-code), using construction X applied to C([0,9]) ⊂ C([0,8]) based on
- linear OA(457, 257, F4, 19) (dual of [257, 200, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 257 | 48−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(449, 257, F4, 17) (dual of [257, 208, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 257 | 48−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(41, 9, F4, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 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(458, 238, F4, 2, 19) (dual of [(238, 2), 418, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(458, 238, F4, 3, 19) (dual of [(238, 3), 656, 20]-NRT-code) | [i] | ||
| 3 | Digital (39, 58, 238)-net over F4 | [i] | ||