Information on Result #679138
Linear OA(4104, 16410, F4, 19) (dual of [16410, 16306, 20]-code), using construction X applied to Ce(18) ⊂ Ce(14) based on
- linear OA(499, 16384, F4, 19) (dual of [16384, 16285, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(478, 16384, F4, 15) (dual of [16384, 16306, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(45, 26, F4, 3) (dual of [26, 21, 4]-code or 26-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), 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(4104, 10618, F4, 2, 19) (dual of [(10618, 2), 21132, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4104, 10618, F4, 3, 19) (dual of [(10618, 3), 31750, 20]-NRT-code) | [i] | ||
| 3 | Digital (85, 104, 10618)-net over F4 | [i] | ||
| 4 | Linear OOA(4104, 8205, F4, 2, 19) (dual of [(8205, 2), 16306, 20]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4104, 5470, F4, 3, 19) (dual of [(5470, 3), 16306, 20]-NRT-code) | [i] | ||
| 6 | Linear OOA(4104, 1823, F4, 19, 19) (dual of [(1823, 19), 34533, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |