Information on Result #680498
Linear OA(417, 1031, F4, 5) (dual of [1031, 1014, 6]-code), using construction X4 applied to Ce(4) ⊂ Ce(2) based on
- linear OA(416, 1024, F4, 5) (dual of [1024, 1008, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(411, 1024, F4, 3) (dual of [1024, 1013, 4]-code or 1024-cap in PG(10,4)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(46, 7, F4, 6) (dual of [7, 1, 7]-code or 7-arc in PG(5,4)), using
- dual of repetition code with length 7 [i]
- linear OA(41, 7, F4, 1) (dual of [7, 6, 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(418, 1032, F4, 5) (dual of [1032, 1014, 6]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(418, 1035, F4, 5) (dual of [1035, 1017, 6]-code) | [i] | Varšamov–Edel Lengthening | |
| 3 | Linear OA(418, 1033, F4, 5) (dual of [1033, 1015, 6]-code) | [i] | Construction X with Varšamov Bound | |
| 4 | Linear OOA(417, 515, F4, 3, 5) (dual of [(515, 3), 1528, 6]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |
| 5 | Linear OOA(417, 515, F4, 5, 5) (dual of [(515, 5), 2558, 6]-NRT-code) | [i] | ||