Information on Result #680561
Linear OA(427, 1036, F4, 7) (dual of [1036, 1009, 8]-code), using construction X4 applied to Ce(6) ⊂ Ce(4) based on
- linear OA(426, 1024, F4, 7) (dual of [1024, 998, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- 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, 12, F4, 11) (dual of [12, 1, 12]-code or 12-arc in PG(10,4)), using
- dual of repetition code with length 12 [i]
- linear OA(41, 12, F4, 1) (dual of [12, 11, 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 OOA(427, 1036, F4, 2, 7) (dual of [(1036, 2), 2045, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(427, 1036, F4, 3, 7) (dual of [(1036, 3), 3081, 8]-NRT-code) | [i] | ||
| 3 | Digital (20, 27, 1036)-net over F4 | [i] | ||
| 4 | Linear OA(428, 1044, F4, 7) (dual of [1044, 1016, 8]-code) | [i] | Varšamov–Edel Lengthening | |
| 5 | Linear OA(429, 1072, F4, 7) (dual of [1072, 1043, 8]-code) | [i] | ||
| 6 | Linear OA(430, 1156, F4, 7) (dual of [1156, 1126, 8]-code) | [i] | ||
| 7 | Linear OOA(427, 518, F4, 2, 7) (dual of [(518, 2), 1009, 8]-NRT-code) | [i] | OOA Folding | |