Information on Result #679354
Linear OA(4115, 16417, F4, 21) (dual of [16417, 16302, 22]-code), using construction XX applied to Ce(20) ⊂ Ce(16) ⊂ Ce(14) based on
- linear OA(4106, 16384, F4, 21) (dual of [16384, 16278, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(485, 16384, F4, 17) (dual of [16384, 16299, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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, 29, F4, 3) (dual of [29, 24, 4]-code or 29-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
- linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-code), using
- Reed–Solomon code RS(3,4) [i]
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(4115, 10811, F4, 2, 21) (dual of [(10811, 2), 21507, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4115, 10811, F4, 3, 21) (dual of [(10811, 3), 32318, 22]-NRT-code) | [i] | ||
| 3 | Digital (94, 115, 10811)-net over F4 | [i] | ||