Information on Result #677864
Linear OA(490, 4194329, F4, 11) (dual of [4194329, 4194239, 12]-code), using construction X4 applied to C([0,5]) ⊂ C([0,4]) based on
- linear OA(489, 4194305, F4, 11) (dual of [4194305, 4194216, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 4194305 | 422−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(467, 4194305, F4, 9) (dual of [4194305, 4194238, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 4194305 | 422−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(423, 24, F4, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,4)), using
- dual of repetition code with length 24 [i]
- linear OA(41, 24, F4, 1) (dual of [24, 23, 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(491, 4194330, F4, 11) (dual of [4194330, 4194239, 12]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(492, 4194331, F4, 11) (dual of [4194331, 4194239, 12]-code) | [i] | ||
| 3 | Linear OA(493, 4194332, F4, 11) (dual of [4194332, 4194239, 12]-code) | [i] | ||
| 4 | Linear OA(492, 4194332, F4, 11) (dual of [4194332, 4194240, 12]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OA(493, 4194334, F4, 11) (dual of [4194334, 4194241, 12]-code) | [i] | ||