Information on Result #678927
Linear OA(458, 16401, F4, 11) (dual of [16401, 16343, 12]-code), using construction X4 applied to C([0,5]) ⊂ C([0,4]) based on
- linear OA(457, 16385, F4, 11) (dual of [16385, 16328, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(443, 16385, F4, 9) (dual of [16385, 16342, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(415, 16, F4, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,4)), using
- dual of repetition code with length 16 [i]
- linear OA(41, 16, F4, 1) (dual of [16, 15, 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(459, 16402, F4, 11) (dual of [16402, 16343, 12]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(460, 16403, F4, 11) (dual of [16403, 16343, 12]-code) | [i] | ||
| 3 | Linear OA(461, 16404, F4, 11) (dual of [16404, 16343, 12]-code) | [i] | ||
| 4 | Linear OA(460, 16404, F4, 11) (dual of [16404, 16344, 12]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OA(461, 16406, F4, 11) (dual of [16406, 16345, 12]-code) | [i] | ||
| 6 | Linear OOA(458, 5467, F4, 3, 11) (dual of [(5467, 3), 16343, 12]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(458, 3280, F4, 11, 11) (dual of [(3280, 11), 36022, 12]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |