Information on Result #678288
Linear OA(4128, 262165, F4, 19) (dual of [262165, 262037, 20]-code), using construction X4 applied to C([0,9]) ⊂ C([0,8]) based on
- linear OA(4127, 262145, F4, 19) (dual of [262145, 262018, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(4109, 262145, F4, 17) (dual of [262145, 262036, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(419, 20, F4, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,4)), using
- dual of repetition code with length 20 [i]
- linear OA(41, 20, F4, 1) (dual of [20, 19, 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 OA(4129, 262166, F4, 19) (dual of [262166, 262037, 20]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4130, 262167, F4, 19) (dual of [262167, 262037, 20]-code) | [i] | ||
| 3 | Linear OA(4131, 262168, F4, 19) (dual of [262168, 262037, 20]-code) | [i] | ||
| 4 | Linear OA(4131, 262169, F4, 19) (dual of [262169, 262038, 20]-code) | [i] | Construction X with Varšamov Bound | |