Information on Result #679368
Linear OA(482, 16404, F4, 15) (dual of [16404, 16322, 16]-code), using construction XX applied to Ce(14) ⊂ Ce(12) ⊂ Ce(10) based on
- 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(464, 16384, F4, 13) (dual of [16384, 16320, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(457, 16384, F4, 11) (dual of [16384, 16327, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(41, 17, F4, 1) (dual of [17, 16, 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
- linear OA(41, 3, F4, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-code), using
- Reed–Solomon code RS(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-code), 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(482, 10646, F4, 2, 15) (dual of [(10646, 2), 21210, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(482, 10646, F4, 3, 15) (dual of [(10646, 3), 31856, 16]-NRT-code) | [i] | ||
| 3 | Digital (67, 82, 10646)-net over F4 | [i] | ||
| 4 | Linear OOA(482, 8202, F4, 2, 15) (dual of [(8202, 2), 16322, 16]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(482, 5468, F4, 3, 15) (dual of [(5468, 3), 16322, 16]-NRT-code) | [i] | ||