Information on Result #678296
Linear OA(474, 262165, F4, 11) (dual of [262165, 262091, 12]-code), using construction X4 applied to C([0,5]) ⊂ C([0,4]) based on
- linear OA(473, 262145, F4, 11) (dual of [262145, 262072, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(455, 262145, F4, 9) (dual of [262145, 262090, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (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(475, 262166, F4, 11) (dual of [262166, 262091, 12]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(476, 262167, F4, 11) (dual of [262167, 262091, 12]-code) | [i] | ||
| 3 | Linear OA(477, 262168, F4, 11) (dual of [262168, 262091, 12]-code) | [i] | ||
| 4 | Linear OA(476, 262168, F4, 11) (dual of [262168, 262092, 12]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OA(477, 262170, F4, 11) (dual of [262170, 262093, 12]-code) | [i] | ||