Information on Result #678057
Linear OA(4142, 1048599, F4, 19) (dual of [1048599, 1048457, 20]-code), using construction X4 applied to C([0,9]) ⊂ C([0,8]) based on
- linear OA(4141, 1048577, F4, 19) (dual of [1048577, 1048436, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 420−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(4121, 1048577, F4, 17) (dual of [1048577, 1048456, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 420−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(421, 22, F4, 21) (dual of [22, 1, 22]-code or 22-arc in PG(20,4)), using
- dual of repetition code with length 22 [i]
- linear OA(41, 22, F4, 1) (dual of [22, 21, 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(4143, 1048600, F4, 19) (dual of [1048600, 1048457, 20]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4144, 1048601, F4, 19) (dual of [1048601, 1048457, 20]-code) | [i] | ||
| 3 | Linear OA(4145, 1048602, F4, 19) (dual of [1048602, 1048457, 20]-code) | [i] | ||
| 4 | Linear OA(4145, 1048603, F4, 19) (dual of [1048603, 1048458, 20]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OOA(4142, 349533, F4, 3, 19) (dual of [(349533, 3), 1048457, 20]-NRT-code) | [i] | OOA Folding | |